Question

If A = 5i-7j-3k and = 2i-2j-xk are perpendicular vectors. the value of x is

Answer 1

Answer:

The value of x would be -8

Explanation:

$\vec{A}=5\hat{i}-7\hat{j}-3\hat{k} and \vec{B}=2\hat{i}-2\hat{j}-x\hat{k}$

If the vectors are perpendicular then their dot product will be equal to zero.

$\vec{A}.\vec{B}=5*2+(-7)*(-2)+(-3)*(-x) = 10+14+3x=24+3x\\\\ Now if \vec{A}\perp\vec{B} then \vec{A}.\vec{B}=0\\\\\therefore24+3x=0\\\\\implies3x=-24\\\\\implies x=-\frac{24}{3}=-8$

The value of x would be -8