Question

XY-plane divides the line joining the points A(2, 3, -5) and B(1, -2, -3) in the ratio ______ 

Options

• 3 : 2 externally

• 5 : 3 externally

• 2 : 1 internally

• 5 : 3 internally

Answer 1

XY-plane divides the line joining the points A(2, 3, -5) and B(1, -2, -3) in the ratio 5 : 3 externally.

Explanation:

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

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

z = `(-3k - 5)/(k + 1)`

Since P (x, y, z) lie on the XY plane, its z coordinate will be zero.

∴ `0 = (-3k - 5)/(k + 1)`

⇒ -3k - 5 = 0

⇒ k = `-5/3`