Question

A plane $P$ is perpendicular to the vector ${A}=2 \hat{i}+3 \hat{j}+6 \hat{k}$ and contains the terminal point of the vector ${B}=\hat{i}+5 \hat{j}+3 \hat{k}$. The distance from the origin to the plane $P$, is

• A. 1
• B. 2
• C. 4
• D. 5

Answer 1

Answer: (D)

Plane P passes through $(1,5,3)$ and normal to ${ A }=(2,3,6)$
Equation is $2(x-1)+3(y-5)+6(z-3)=0 \Rightarrow 2 x+3 y+6 z=35$
$\therefore $ Perpendicular from $(0,0,0)$ to the plane $=\left|\frac{-35}{7}\right|=5$