If a vector $2 i + 3 j + 8 k$ is perpendicular to the vector $4 i - 4 j + a k$ , then the value of $a$ is

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Solution

$\to A = 2 i + 3 j + 8 k$
$\to B = 4 i - 4 j + a k$
Since $\to A$ and $\to B$ are perpendicular $\to A . \to B = 0$
$(2 i + 3 j + 8 k) (4 i - 4 j + a k)$
$8 - 12 + 8 a = 0$
$a = \frac{4}{8} = \frac{1}{2}$

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