# RD SHARMA Solutions for Class 12-science Maths Chapter 23 - Algebra of Vectors

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.1

Represent graphically a dispacement of 40 km, 30° east of north.

Represent graphically a displacement of 50 km, south-east

Here, vector represents the displacement of 50 km, south-east.

Represent graphically a displacement of 70 km, 40° north of west.

Here, vector represents the displacement of 70 km, 40° north of west.

Classify the following measures as scalars and vectors.

(i) 15 kg

(ii) 20 kg weight

(iii) 45°

(iv) 10 metres south-east

(v) 50 m/s^{2}

(i) **15 kg** is a scalar quantity because it involves only

(ii) **20 kg weight** is a vector quantity as it involves both magnitude and direction.

(iii) **45°** is a scalar quantity as it involves only magnitude.

(iv) **10 metres south-east is a vector quantity as it involve direction.**

(v) 50 m/s^{2} is a **scalar** quantity as it involves magnitude of** acceleration.**

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.2

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.3

Find the position vector of a point R which divides the line joining the two points P and Q with position vectors

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.4

Prove by vector method that the internal bisectors of the angles of a triangle are concurrent.

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.5

Find |AB| in each case.

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.6

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.7

Using vectors, find the value of λ such that the points

(λ, - 10, 3), (1 -1, 3) and (3, 5, 3) are collinear.

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.8

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.9

If a unit vector makes and angles and an acute angle θ with , then find θ and hence, the components of .

## Chapter 23 - Algebra of Vectors Exercise MCQ

If in a Δ ABC, A = (0, 0), B = (3, 3), = (-3, 3), then the vector of magnitude 2 units directed along AO, where O is the circumcentre of Δ ABC is

Correct option:(a)

Correct option:(c)

- C is a mid-point of AB
- C divides AB in the ratio 2:1
- 3 AC = 5CB
- 2 AC = 3CB

Correct option: (c)

Correct option: (d)

- 40
- -40
- 20
- -20

Correct option: (b)

Correct option: (b)

- Null vector
- Unit vector
- Constant vector
- None of these

Correct option: (b)

Correct option: (c)

Correct option: (b)

Correct option: (b)

- Rhombus
- Rectangle
- Square
- Parallelogram

Correct option: (d)

Correct option: (a)

NOTE: Answer not matching with back answer.

Correct option: (d)

- form an isosceles triangle
- form a right triangle
- are collinear
- form a scalene triangle

Correct option: (a)

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

Correct option: (a)

Correct option: (c)

Correct option: (d)

If a and b are two collinear vectors, then which of the following are incorrect?

Correct option: (d)

In Figure 23.67, which of the following is not true?

Correct option: (c)

## Chapter 23 - Algebra of Vectors Exercise Ex. 23VSAQ

Define position vector of a point.

If are position vectors of the points *A, B* and *C* respectively, write the value of

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