Mathematics - Vector Question with Solution | TestHub

Point is $(-1,2,6)$ Line passes through the point $(2,3,-4)$ parallel to vector whose direction ratios is $6,3,-4$. Equation is $\frac{x-2}{6}=\frac{y-3}{3}=\frac{z+4}{-4}=\lambda$ Any point on this line is given by $x=6$ $\lambda +2,y=3\lambda +3,z=-4\lambda -4$ Now, d. Rs of line passing through $(-1,2,6)$ and $\perp$ to this line is $\{(x+1),(y-2),(z-6)\}$ So, $6(x+1)+3(y-2)-4(z-6)=0$ $\Rightarrow 6x+3y-4z+24=0$ Now, $6(6\lambda +2)+3(3\lambda +3)+4(4\lambda +4)$ $+24=0$ $\Rightarrow 61\lambda +61=0\Rightarrow \lambda =-1$ So, $x=-4,y=0,z=0$ Now, distance between $(-1,2,6)$ and $(-4,0,0)$ is $\sqrt{9+4+36}=\sqrt{49}=7$