Question

If the origin and the points P(2, 3, 4), Q(1, 2, 3) and R(x, y, z) are coplanar, then ______.

Options

• x – 2y – z = 0

• x + 2y + z = 0

• x – 2y + z = 0

• 2x – 2y + z = 0

Answer 1

If the origin and the points P(2, 3, 4), Q(1, 2, 3) and R(x, y, z) are coplanar, then x – 2y + z = 0.

Explanation:

We have, O(0, 0, 0), P(2, 3, 4), Q(1, 2, 3) and R(x, y, z) are coplanar.

So, `|(x - 0, y - 0, z - 0),(2 - 0, 3 - 0, 4 - 0),(1 - 0, 2 - 0, 3 - 0)|` = 0

`\implies |(x, y, z),(2, 3, 4),(1, 2, 3)|` = 0

`\implies` x(9 – 8) – y(6 – 4) + z(4 – 3) = 0

`\implies` x – 2y + z = 0