Question

If a plane passes through the point $\left(1 , 1 , 1\right)$ and is perpendicular to the line $\frac{x - 1}{3}=\frac{y - 1}{0}=\frac{z - 1}{4}$ , then its perpendicular distance from the origin is-

• A. $\frac{3}{4}$
• B. $\frac{4}{3}$
• C. $\frac{7}{5}$
• D. $1$

Answer 1

Answer: (C)

Equation of the plane which passes through $\left(1 , 1 , 1\right)$ and dr’s of its normal are $3,0,4$ is-
$3\left(x - 1\right)+0\left(y - 1\right)+4\left(z - 1\right)=0$
$3x+4z-7=0$
Perpendicular distance from the origin is-
$=\left|\frac{- 7}{5}\right|=\frac{7}{5}$