Question

If points P(4, 5, x), Q(3, y, 4) and R(5, 8, 0) are collinear, then the value of x + y is ______.

Options

• – 4

• 3

• 5

• 4

Answer 1

If points P(4, 5, x), Q(3, y, 4) and R(5, 8, 0) are collinear, then the value of x + y is 4.

Explanation:

`vec(PQ)` = (–1, y – 5, 4 – x)

`vec(QR)` = (2, 8 – y, – 4)

∵ P, Q, R are collinear

∴ `(-1)/2 = (y - 5)/(8 - y) = (4 - x)/(-4)`

`\implies` –8 + y = 2y – 10 and 4 = 8 – 2x

`\implies` y = 2 and x = 2

∴ x + y = 4