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Vector Algebra

Question
CBSEENMA12034067
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Find straight lambda if the vectors 5 straight i with hat on top plus 2 straight j with hat on top minus straight k with hat on top and straight lambda straight i with hat on top space minus space straight j with hat on top space plus space 5 space straight k with hat on top are orthogonal.

Solution

Let straight a with rightwards arrow on top space equals space 5 straight i with hat on top plus 2 straight j with hat on top space minus straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space straight lambda straight i with hat on top space minus space straight j with hat on top space plus space 5 space straight k with hat on top
        straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space left parenthesis 5 right parenthesis thin space left parenthesis straight lambda right parenthesis plus left parenthesis 2 right parenthesis thin space left parenthesis negative 1 right parenthesis space plus space left parenthesis negative 1 right parenthesis space left parenthesis 5 right parenthesis space equals space 5 space straight lambda minus 2 minus 5 space equals 5 straight lambda minus 7
because space space space space straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space are space orthogonal therefore space space space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 0 space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space 5 space straight lambda space minus space 7 space equals space 0 space space space space space rightwards double arrow space space space straight lambda space equals space 7 over 5.

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