Question

Find the direction ratios of a line perpendicular to the two lines whose direction rations are
(i) -2, 1, -1 and -3, -4, 1

Answer 1

The given lines are $-2\hat{i}+\hat{j}-\hat{k}$ and $-3\hat{i}-4\hat{j}+\hat{k}$.

Now, we find the line perpendicular to the two lines :

$\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ -2& 1& -1\\ -3& -4& 1\end{array}\right|$ = $\hat{i}(1-4)-\hat{j}(-2-3)+\hat{k}(8+3)$

$=-3\hat{i}+5\hat{j}+11\hat{k}$

Thus, the direction ratios of the required line are $-3,5,11$.