Question

If the origin and the points P(2, -7, 5), Q(2, 3, - 5) and R(x, y, z) are co-planar, then ______ 

Options

• x + y + z = 0

• x - y + z = 0

• x - 2y + z = 0

• x - y + 2z = 0

Answer 1

If the origin and the points P(2, -7, 5), Q(2, 3, - 5) and R(x, y, z) are co-planar, then x + y + z = 0.

Explanation:

Since O(0, 0, 0), P(2, -7, 5), Q(2, 3, -5), R(x, y, z) are co-planar,

`[overline(OR)   overline(OP)   overline(OQ)] = 0`

⇒ `|(x, y, z), (2, -7, 5), (2, 3, -5)| = 0`

⇒ x (35 - 15) - y (-10 - 10) + z (6 + 14) = 0

⇒ x + y + z = 0