If A and B are two perpendicular vectors given by $¯ ¯¯ ¯ A = 5 ¯ i + 7 ¯ j + 3 ¯ ¯ ¯ k$ , and $4 ¯ ¯¯ ¯ B = 2 ¯ i + 2 ¯ j + c ¯ ¯ ¯ k$ , then the value of $c$ is:

-2

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-7

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-8

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Solution

The correct option is C -8
Given $\to A = 5^i + 7^j + 3^k$
$4 \to B = 2^i + 2^j + c^k$
$\to B = \frac{2}{4}^i + \frac{2}{4}^j + \frac{c}{4}^k$

As given vectors are perpendicular to each other so their dot product must be zero.
Therefore: $\to A . \to B = 0$
$(5^i + 7^j + 3^k) . (0.5^i + 0.5^j + \frac{c}{4}^k) = 0$
$2.5 + 3.5 + \frac{3}{4} c = 0$
$\frac{3}{4} c = - 6$
$c = \frac{- 24}{3}$
$c = - 8$

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