Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Three-dimensional Geometry

Question:

If from a point (a, b, c) perpendicular PA, PB are drawn to YZ and ZX planes, then the equation of the plane OAB is 

Options:

$bcx + cay + abz = 0$

$bcx + cay + abz = 0$

$bcx - cay + abz = 0$

$-bcx + cay + abz = 0$

Correct Answer:

$bcx + cay + abz = 0$

Explanation:

The coordinates of A and B are (0, b, c) and (a, 0, c) respectively.

The equation of a plane passing through O(0, 0, 0) is

$Px + Qy + Rz = 0 $ ..........(i)

It passes through A and B

$∴ P × 0 + Q ×  b + R × c = 0 $

and, $ P × a + Q × 0 + R × c = 0 $

$⇒ \frac{P}{bc}=\frac{Q}{ac}=\frac{R}{-ab}$

Substituting the values of P, Q and R in (i), we get

$bcx + cay + abz = 0$