Question

Find a vector of magnitude $18$ which is perpendicular to both the vectors, $4\hat{i}-\hat{j}+3\hat{k}$ and $-2\hat{i}+\hat{j}-2\hat{k}$.

• A. $-8\hat{i}+12\hat{j}+12\hat{k}$.
• B. $-7\hat{i}+12\hat{j}+12\hat{k}$.
• C. $-6\hat{i}+12\hat{j}+12\hat{k}$.
• D. $-9\hat{i}+12\hat{j}+12\hat{k}$.

Answer 1

The correct option is C $-6\hat{i}+12\hat{j}+12\hat{k}$.

A vector perpendicular to the given two vectors will be in the direction of their cross product. The unit vector in the direction of their cross product will be( cross product can be found by using

the method of determinant

$\frac{-i+2j+2k}{\sqrt{{-1}^2+2^2+2^2}}=\frac{-i+2j+2k}{3}$

$=\frac{18}{3}(-i+2j+2k)=-6i+12j+12k$