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Vector Algebra

Question
CBSEENMA12033946
Wired Faculty App

Vectors drawn from the origin to the points A, B and C are respectively straight a with rightwards arrow on top. space straight b with rightwards arrow on top space and space 4 space straight a with rightwards arrow on top space space minus space 3 space straight b with rightwards arrow on top. Find AC with rightwards arrow on top space and space BC with rightwards arrow on top.

Solution

Let O be origin of vectors. Then
                          OA with rightwards arrow on top space equals straight a with rightwards arrow on top comma space space OB with rightwards arrow on top space equals space straight b with rightwards arrow on top comma space space OC with rightwards arrow on top space equals space 4 space straight a with rightwards arrow on top space minus space 3 space straight b with rightwards arrow on top
Now,              AC with rightwards arrow on top space equals space OC with rightwards arrow on top space minus space OA with rightwards arrow on top space equals space open parentheses 4 space straight a with rightwards arrow on top minus space 3 space straight b with rightwards arrow on top close parentheses space minus space straight a with rightwards arrow on top space equals space 3 space straight a with rightwards arrow on top space minus space 3 space straight b with rightwards arrow on top
and                BC with rightwards arrow on top space equals space OC with rightwards arrow on top space minus space OB with rightwards arrow on top space equals space left parenthesis 4 space straight a with rightwards arrow on top space minus space 3 space straight b with rightwards arrow on top right parenthesis space minus space straight b with rightwards arrow on top space equals space 4 space straight a with rightwards arrow on top space minus space 4 space straight b with rightwards arrow on top

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