Question

The distance of the point having position vector $-\hat{i}+2\hat{j}+6\hat{k}$ from the straight line passing through the point $(2,3,-4)$ and parallel to the vector, $6\hat{i}+3\hat{j}-4\hat{k}$ is

Answer 1

Answer: 7

Equation of the line is $\frac{x-2}{6}=\frac{y-3}{3}=\frac{z+4}{-4}$

Let the point M on the line $l$ is $(6\lambda +2,3\lambda +3,-4\lambda -4)$
Direction ratio’s of PM is $(6\lambda +3,3\lambda +1,-4\lambda -10)$
$\Rightarrow (6\lambda +3)(6)+(3\lambda +1)(3)+(-4\lambda -10)(-4)=0$
$\Rightarrow \lambda =-1$
$\Rightarrow M$ is $(-4,0,0)$
$\therefore PM=\sqrt{9+4+36}=7$