Question

If a vector 2i + 3j + 8k is perpendicular to vector – 4i + 6j + ak. Find the value of a ?
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Answer 1

Explanation:

when vector are perpendicular than their dot products is zero.

let

vector (a)=2i + 3j + 8k

vector (b) = – 4i + 6j + ak

$vector(a). \: vector(b) = 0 \\ (2i + 3j + 8k).( - 4i + 6j + ak) = 0 \\ \\ - 8 + 18 + 8a = 0 \\ \\ 10 + 8a = 0 \\ \\ 8a = - 10 \\ \\ a = \frac{ - 10}{8} \\ \\ a = \frac{ - 5}{4}$