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Vector Algebra

Question
CBSEENMA12034000
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Find the condition that the vectors straight a with rightwards arrow on top space equals space straight k space straight i with hat on top space plus space straight l space straight j with hat on top space and space straight b with rightwards arrow on top space equals space straight l space straight i with hat on top space plus space straight k space straight j with hat on top comma space space left parenthesis straight k comma space straight l space not equal to 0 right parenthesis space are space parallel

Solution

Here,   straight a with rightwards arrow on top space equals space straight k space straight i with hat on top space plus space straight l space straight j with hat on top comma space space straight b with rightwards arrow on top space equals space straight l space straight i with hat on top space plus space straight k space straight j with hat on top
Let straight a with rightwards arrow on top space and space straight b with rightwards arrow on top be parallel.
therefore space  there exists a non-zero scalar straight lambda such that straight a with rightwards arrow on top space equals space straight lambda space straight b with rightwards arrow on top
therefore space space space straight k space straight i with hat on top space plus space straight l space straight j with hat on top space equals space straight lambda space li with rightwards arrow on top space plus space λk straight j with rightwards arrow on top therefore space space left parenthesis straight k minus straight lambda space straight l right parenthesis space straight i with hat on top space plus space left parenthesis straight l minus straight lambda space straight k right parenthesis space straight j with hat on top space equals space 0 with rightwards arrow on top rightwards double arrow space space straight k space minus space straight lambda space straight l space equals space 0 comma space space space space straight l space minus straight lambda space straight k space equals space 0 rightwards double arrow space space space space straight lambda space equals space straight k over straight l comma space straight lambda space equals space straight l over straight k
Equating values of straight lambda comma we get,
                         straight k over straight l space equals space straight l over straight k space space space or space space space straight k squared space equals space straight l squared
which is required condition. 

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