Question

The line passing through the points (5, 1, a) and (3, b, 1) crosses the YZ – plane at the point `(0, 17/2, (-13)/2)`, then ______.

Options

• a = 2, b = 8

• a = 4, b = 6

• a = 6, b = 4

• a = 8, b = 2

Answer 1

The line passing through the points (5, 1, a) and (3, b, 1) crosses the YZ – plane at the point `(0, 17/2, (-13)/2)`, then a = 6, b = 4.

Explanation:

Equation of the line passing through the points (5, 1, a) and (3, b, 1) is

`(x - 3)/(5 - 3) = (y - "b")/(1 - "b") = (z - 1)/("a" - 1)`  ......(i)

The line passes through the point `(0, 17/2, (-13)/2)`

∴ `(-3)/2 = (17/2 - "b")/(1 - "b") = ((-13)/2 - 1)/("a" - 1)` .....[From (i)]

∴ a – 1 = `((-15)/2)/((-3)/2)` = 5

∴ a = 5 + 1 = 6 and –3 + 3b = 17 – 2b

∴ 5b = 20 ⇒ b = 4

∴ a = 6, b = 4