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Vector Algebra

Question
CBSEENMA12034064
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For what values of A are the vectors 
straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight lambda space straight j with hat on top space plus space straight k with hat on top space and space straight b with rightwards arrow on top space equals space straight i with hat on top space minus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top perpendicular to each other?

Solution
Here
          straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight lambda space straight j with hat on top space plus space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space straight i with hat on top space minus space 2 space straight j with hat on top space plus space 3 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 2 right parenthesis space left parenthesis 1 right parenthesis space plus space left parenthesis straight lambda right parenthesis space left parenthesis negative 2 right parenthesis space plus space left parenthesis 1 right parenthesis thin space left parenthesis 3 right parenthesis space equals space 2 space minus space 2 space straight lambda space plus space 3 space equals space minus 2 space straight lambda space plus space 5
because space space space space space straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space are space perpendicular space to space each space other 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 rightwards double arrow space space space minus 2 straight lambda space plus 5 space equals space space 0 space space space rightwards double arrow space space space 2 space straight lambda space equals 5 therefore space space space space space space space space space space straight lambda space equals space 5 over 2

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