Question

The XZ plane divides the line segment joining the points (3, 2, b) and (a, -4, 3) in the ratio ______.

Options

• 1 : 2

• 2 : 3

• 3 : 1

• 4 : 3

Answer 1

The XZ plane divides the line segment joining the points (3, 2, b) and (a, -4, 3) in the ratio 1 : 2.

Explanation:

Let the XZ plane divides the line segment joining the given points in the ratio k : 1 at the point P (x, y, z).

∴ x = `("ka" + 3)/("k" + 1), "y" = (- 4"k" + 2)/("k + 1")`

z = `(3"k" + "b")/("k + 1")`

Since P (x, y, z) lie on the XZ plane, its y co-ordinate will be zero.

∴ 0 = `(- 4"k" + 2)/("k + 1")`

⇒ - 4k + 2 = 0

⇒ k = `1/2`

∴ k : 1 = 1 : 2