lf a vector $¯ ¯¯ ¯ A = 2 ¯ i + 2 ¯ j + 3 ¯ ¯ ¯ k$ and $¯ ¯¯ ¯ B = 3 ¯ i + 6 ¯ j + n ¯ ¯ ¯ k$ , are perpendicular to each other, then the value of 'n' is:

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-6

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Solution

The correct option is D -6
If two vectors are perpendicular to each other then their scalar(dot) product must be zero.
Therefore, $¯ ¯¯ ¯ A . ¯ ¯¯ ¯ B = 0$
$(2^i + 2^j + 3^k) \cdot (3^i + 6^j + n^k) = 0$
$6 + 12 + 3 n = 0$
$3 n = - 18$
$n = - 6$

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