RD SHARMA Solutions for Class 11-science Maths Chapter 28 - Introduction to 3-D coordinate geometry

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Chapter 28 - Introduction to 3-D coordinate geometry Exercise Ex. 28.1

Question 1(i)

Name the octants in which the following points lie:

 (i) (5, 2, 3)

 

 

 

 

 

 

 

Solution 1(i)

All are positive, so octant is XOYZ

 

Question 1(ii)

Name the octants in which the following points lie:

(ii) (-5, 4, 3)

 

 

Solution 1(ii)

X is negative and rest are positive, so octant is X'OYZ

Question 1(iii)

Name the octants in which the following points lie:

(4, -3, 5)

 

 

Solution 1(iii)

Y is negative and rest are positive, so octant is XOY'Z

Question 1(iv)

Name the octants in which the following points lie:

(7, 4, -3)

 

 

Solution 1(iv)

Z is negative and rest are positive, so octant is XOYZ'

Question 1(v)

Name the octants in which the following points lie:

(-5, -4, 7)

 

 

Solution 1(v)

X and Y are negative and Z is positive, so octant is X'OY'Z

Question 1(vi)

Name the octants in which the following points lie:

(-5, -3, -2)

 

 

Solution 1(vi)

All are negative, so octant is X'OY'Z'

Question 1(vii)

Name the octants in which the following points lie:

(2, -5, -7)

 

 

Solution 1(vii)

Y and Z are negative, so octant is XOY'Z'

Question 1(viii)

Name the octants in which the following points lie:

(-7, 2, -5)

 

 

Solution 1(viii)

X and Z are negative, so octant is X'OYZ'

Question 2(i)

Find the image of :

(-2, 3, 4) in the yz-plane 

Solution 2(i)

YZ plane is x-axis, so sign of x will be changed. So answer is (2, 3, 4)

Question 2(ii)

Find the image of :

(-5, 4, -3) in the xz-plane. 

Solution 2(ii)

XZ plane is y-axis, so sign of y will be changed. So answer is (-5, -4, -3)

Question 2(iii)

Find the image of :

(5, 2, -7) in the xy-plane 

Solution 2(iii)

XY-plane is z-axis, so sign of Z will change. So answer is (5, 2, 7)

Question 2(iv)

Find the image of :

(-5, 0, 3) in the xz-plane 

Solution 2(iv)

XZ plane is y-axis, so sign of Y will change, So answer is (-5, 0, 3)

Question 2(v)

Find the image of :

(-4, 0, 0) in the xy-plane 

Solution 2(v)

XY plane is Z-axis, so sign of Z will change So answer is (-4, 0, 0)

Question 3

A cube of side 5 has one vertex at the point (1, 0, -1), and the three edges from this vertex are, respectively, parallel to the negative x and y axes and positive z-axis. Find the value coordinates of the other vertices of the cube. 

Solution 3

Vertices of cube are

(1, 0, -1) (1, 0, 4) (1, -5, -1)

(1, -5, 4) (-4, 0, -1) (-4, -5, -4)

(-4, -5, -1) (4, 0, 4) (1, 0, 4)

Question 4

Planes are drawn parallel to the coordinate planes through the points (3, 0, -1) and (-2, 5, 4). Find the lengths of the edges of the parallelepiped so formed. 

Solution 4

3-(-2)=5, |0-5|=5, |-1-4|=5

5, 5, 5 are lengths of edges

Question 5

Planes are drawn through the points (5, 0, 2) and (3, -2, 5) parallel to the coordinate planes. Find the lengths of the edges of the rectangular parallelepiped so formed. 

Solution 5

5-3=2, 0-(-2)=2, 5-2=3

2, 2, 3 are lengths of edges

Question 6

Find the distances of the point p(-4, 3, 5) from the coordinate axes. 

Solution 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

Question 7

The coordinate of a point are (3, -2, 5). Write down the coordinates of seven points such that the absolute values of their coordinates are the same as those of the coordinates of the given point. 

Solution 7

(-3, -2, -5) (-3, -2, 5) (3, -2, -5) (-3, 2, -5) (3, 2, 5)

(3, 2, -5) (-3, 2, 5)

Chapter 28 - Introduction to 3-D coordinate geometry Exercise Ex. 28.2

Question 1

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 1

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 3(i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 3(i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 3(ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 3(ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 3(iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 3(iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 4(i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 4(i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 4(ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 4(ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 4(iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 4(iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 7

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 7

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 8

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 8

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 9

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 9

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 10

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 10

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 11

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 11

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 12

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 12

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 13

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 13

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 14

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 14

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 15

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 15

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 16

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 16

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 17

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 17

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 18

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 18

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 19

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 19

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 20(i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 20(i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 20(ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 20(ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 20(iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 20(iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 21

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 21

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 22

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 22

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 23

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Solution 23

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Question 20(iv)

Verify the following

(5, -1, 1), (7, -4, 7), (1, -6, 10) and (-1, -3, 4) are the vertices of a rhombus.

Solution 20(iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry 

Question 24

Find the equation of the set of the points P such that its distances from the points A(3, 4, -5) and B(-2, 1, 4) are equal.

Solution 24

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

Chapter 28 - Introduction to 3-D coordinate geometry Exercise Ex. 28.3

Question 1

The vertices of the triangle are A(5, 4, 6), B(1, -1, 3) and C(4, 3, 2). The internal bisector of angle A meets BC at D. Find the coordinates of D and the Length AD. 

Solution 1

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry 

Question 2

A point C with z-coordinate 8 lies on the line segment joining the points A(2, -3, 4) and B(8, 0, 10). Find its coordinates. 

Solution 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

 

 

 

 

 

Question 3

Show that three points A(2, 3, 4), B(-1, 2, -3) and C(-4, 1, -10) are collinear and find the ratio in which C divides AB. 

Solution 3

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

 

 

Question 4

Find the ratio in which the line joining (2, 4, 5) and (3, 5, 4) is divided by the yz-plane. 

Solution 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

Question 5

Find the ratio in which the line segment joining the points (2, -1, 3) and (-1, 2, 1) is divided by the plane

x+ y + z = 5. 

Solution 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

 

 

Question 6

If the points A(3, 2, -4), B(9, 8, -10) and C(5, 4, -6) are collinear, find the ratio in which C divides AB. 

Solution 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

Question 7

The mid-points of the sides of a triangle ABC are given by (-2, 3, 5), (4, -1, 7) and (6, 5, 3). Find the coordinates of A, B and C. 

Solution 7

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry 

 

 

 

 

 

 

 

 

 

Question 8

A(1, 2, 3), B(0, 4, 1), C(-1, -1, -3) are the vertices of a triangle ABC. Find the point in which the bisector of the angle Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry meets BC. 

Solution 8

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

 

 

Question 9

Find the ratio in which the sphere x2+y2 +z2 = 504 divides the line joining the points (12, -4, 8) and (27, -9, 18). 

Solution 9

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

 

 

 

 

 

 

 

Question 10

Show that the plane ax + by + cz + d = 0 divides the line joining the points (x1,y1,z1) and (x2,y2,z2) in the ratio -Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

Solution 10

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

 

 

 

Question 11

Find the centroid of a triangle, mid-points of whose sides are (1, 2, -3), (3, 0, 1) and (-1, 1, -4). 

Solution 11

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

 

 

Question 12

The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinate of A and B are (3, -5, 7) and (-1, 7, -6) respectively, find the coordinates of the point C. 

Solution 12

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

 

 

 

 

Question 13

Find the coordinates of the points which tisect the line segment joining the points P(4, 2, -6) and Q(10, -16, 6). 

Solution 13

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

 

Question 14

Using section formula, show that the points A(2, -3, 4), B(-1, 2, 1) and C(0, 1/3, 2) are collinear. 

Solution 14

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

 

Question 15

Given that P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) are collinear. Find the ratio in which Q divides PR. 

Solution 15

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry

 

 

 

 

 

 

 

Question 16

Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, -8) is divided by the yz-plane. 

Solution 16

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Introduction To 3 D Coordinate Geometry