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Vector Algebra

Question
CBSEENMA12034068
Wired Faculty App

If straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals negative straight i with hat on top space plus space 2 space straight j with hat on top space plus space straight k with hat on top space space and space straight c with rightwards arrow on top space equals 3 straight i with hat on top space plus space straight j with hat on top such that straight a with rightwards arrow on top space plus space straight lambda straight b with rightwards arrow on top is perpendicular to straight c with rightwards arrow on top, then find the value of straight lambda.

Solution

         straight a with rightwards arrow on top space equals 2 space straight i with hat on top space plus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space minus straight i with hat on top space plus space 2 space straight j with hat on top space plus space straight k with hat on top comma space space straight c with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space straight j with hat on top
therefore space space space space straight a with rightwards arrow on top space plus space straight lambda straight b with rightwards arrow on top space equals space left parenthesis 2 space minus space straight lambda right parenthesis straight i with hat on top space plus space 2 space left parenthesis 1 space plus straight lambda right parenthesis space straight j with hat on top space plus left parenthesis 3 plus straight lambda right parenthesis space straight k with hat on top
Since straight a with rightwards arrow on top plus straight lambda straight b with rightwards arrow on top is perpendicular to straight c with rightwards arrow on top
therefore space space space left parenthesis straight a with rightwards arrow on top space plus space straight lambda straight b with rightwards arrow on top right parenthesis. space straight c with rightwards arrow on top space equals space 0
therefore space space space space left parenthesis 2 minus straight lambda right parenthesis space left parenthesis 3 right parenthesis space plus space 2 space left parenthesis 1 plus straight lambda right parenthesis space left parenthesis 1 right parenthesis space plus space left parenthesis 3 space plus straight lambda right parenthesis space left parenthesis 0 right parenthesis space equals 0 therefore space space space space space 6 minus 3 straight lambda space plus 2 space plus space 2 straight lambda space equals space 0 space space space space space space space space rightwards double arrow space space space space space space straight lambda space equals space 8.

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