Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Three-dimensional Geometry

Question:

The distance of the point (2, 1, 0) from the plane $2x + y + 2z + 5 = 0,$ is

Options:

$\frac{10}{3}$

$\frac{5}{3}$

$\frac{10}{9}$

none of these

Correct Answer:

$\frac{10}{3}$

Explanation:

We know that the distance of the point $(x_1, y_1, z_1)$ from the plane $ax + by + cz + d= 0 $ is

$\frac{ax_1+by_1+cz_1+d}{\sqrt{a^2 + b^2 + c^2}}$

So, required distance $=\frac{|2×2+1+2×0+5|}{\sqrt{2^2 +1^2 +2^2}}=\frac{10}{3}$