For what value of a, the vector s `(2hati - 3hatj + 4hatk)` and `(ahati + 6hatj - 8hatk)` collinear ?

For what value of a, the vector s `(2hati - 3hatj + 4hatk)` and `(ahat

1.	For what value of a, the vector s `(2hati - 3hatj + 4hatk)` and `(ahati + 6hatj - 8hatk)` collinear ?
Answer» The given vectors are collinear only when `(ahati + 6hatj - 8hatk) = lambda(2hati - 3hatj + 4hatk)` for some nonzero scalar `lambda` . Now, `ahati + 6hatj - 8hatk = 2lambda hati - 3lambda hatj + 4lambdahatk` `hArr 2lambda = a , - 3lambda = 6` and `4lambda = - 8`. `hArr = a/2` and `lambda = - 2 hArr a/2= - 2 hArr a = - 4` Hence the given vectors are collinear when `a = - 4`.

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