Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Linear Programming

Question:

The equation of perpendicular from the point (1, 0, 1) to the plane x - y + z = 4 is

Options:

$\frac{x-1}{2}=\frac{y}{-1}=\frac{z-1}{2}$

$\frac{x-1}{1}=\frac{y}{-1}=\frac{z-1}{1}$

$\frac{x-1}{1}=\frac{y-3}{-1}=\frac{z-2}{1}$

$\frac{x-1}{2}=\frac{y}{1}=\frac{z-1}{3}$

Correct Answer:

$\frac{x-1}{1}=\frac{y}{-1}=\frac{z-1}{1}$

Explanation:

The correct answer is Option (3) → $\frac{x-1}{1}=\frac{y}{-1}=\frac{z-1}{1}$

Point: $P(1, 0, 1)$

plane: $x - y + z = 4$

Normal vector = $\hat i-\hat j+\hat k=\vec n$

so line is perpendicular to plane in direction of $\vec n$ and passes through P

line: $\frac{x-1}{1}=\frac{y}{-1}=\frac{z-1}{1}$