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Vector Algebra

Question
CBSEENMA12035694
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Find the value of 'p' for which the vectors 3 straight i with hat on top plus 2 straight j with hat on top plus 9 straight k with hat on top space and space straight i with hat on top minus 2 straight p straight j with hat on top plus 3 straight k with hat on top are parallel.

Solution

Since the vectors are parallel, we have
straight a with rightwards harpoon with barb upwards on top equals straight lambda straight b with rightwards harpoon with barb upwards on top
rightwards double arrow 3 straight i with hat on top plus 2 straight j with hat on top plus 9 straight k space equals space straight lambda open parentheses straight i minus 2 straight p straight j with hat on top space plus 3 straight k close parentheses rightwards double arrow 3 straight i with hat on top plus 2 straight j with hat on top plus 9 straight k space equals space straight lambda straight i with hat on top minus 2 λp straight j with hat on top plus 3 λk Comparing space the space respective space coefficients comma space we space have rightwards double arrow space space straight lambda space equals space 3 semicolon minus 2 λp space equals space 2 rightwards double arrow negative 2 cross times 3 cross times straight p space equals space 2 rightwards double arrow straight p equals fraction numerator negative 1 over denominator 3 end fraction

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