The magnitudes of vectors OA, OB & OC in figure are equal

Asked by brijk456 | 31st Jul, 2019, 10:21: AM

Expert Answer:

begin mathsize 16px style stack OA space with rightwards arrow on top space equals space Acos 30 degree straight i space plus space Asin 30 degree straight j
stack OB space with rightwards arrow on top space equals space Bcos 60 degree straight i space minus space Bsin 60 degree straight j
stack OC space with rightwards arrow on top space equals space minus Ccos 45 degree straight i space plus space Csin 45 degree straight j

Given space that colon space straight A space equals space straight B space equals space straight C
stack OA space with rightwards arrow on top space plus space stack bold OB bold space with bold rightwards arrow on top minus space stack OC space with rightwards arrow on top space
equals space straight A space cos 30 degree straight i space plus space Asin 30 degree straight j space plus space Bcos 60 degree straight i space minus space Bsin 60 degree straight j space plus space Csin 45 degree straight j space plus space minus Ccos 45 degree straight i space
equals space straight A open parentheses cos 30 degree space plus cos 60 degree space minus cos 45 degree space close parentheses straight i space plus space straight A open parentheses sin 30 degree minus sin 60 degree space plus sin 45 degree space close parentheses straight j
equals straight A open parentheses fraction numerator square root of 3 over denominator 2 end fraction plus space 1 half minus space fraction numerator 1 over denominator square root of 2 end fraction close parentheses straight i space plus space straight A open parentheses fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction minus space fraction numerator begin display style square root of 3 end style over denominator begin display style 2 end style end fraction plus space fraction numerator begin display style 1 end style over denominator begin display style square root of 2 end style end fraction close parentheses straight j
rightwards double arrow tanθ space equals space straight y over straight x equals space fraction numerator open parentheses fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction minus space fraction numerator begin display style square root of 3 end style over denominator begin display style 2 end style end fraction plus space fraction numerator begin display style 1 end style over denominator begin display style square root of 2 end style end fraction close parentheses over denominator open parentheses fraction numerator square root of 3 over denominator 2 end fraction plus space 1 half minus space fraction numerator 1 over denominator square root of 2 end fraction close parentheses end fraction space equals space fraction numerator 1 space minus space square root of 3 space plus space square root of 2 over denominator square root of 3 begin display style space end style begin display style plus end style begin display style space end style begin display style 1 end style begin display style space end style begin display style minus end style begin display style space end style begin display style square root of 2 end style end fraction

space space space space space space space space space space space space space space space space space space space space space space space end style

Answered by Yasmeen Khan | 31st Jul, 2019, 03:27: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.