Question

A point P (x, y, z) lies on the line joining points A (1, 2, 3) and B (2, 10, 1). If x co-ordinates of the point P is -1, then ______ 

Options

• y = -14, z = 7

• y = 7 ,z = -14

• y = -1, z = -1

• y = 26, z = -3

Answer 1

A point P (x, y, z) lies on the line joining points A (1, 2, 3) and B (2, 10, 1). If x co-ordinates of the point P is -1, then y = -14, z = 7.

Explanation:

Let P(x, y, z) divide the line joining the points A and B in the ratio λ : 1 internally.

∴ (x, y, z) = `((2lambda + 1)/(lambda + 1), (10lambda + 2)/(lambda + 1), (lambda + 3)/(lambda + 1))`

∴ x = `(2lambda + 1)/(lambda + 1)= -1 ⇒ lambda = (-2)/3`

`y = (10lambda + 2)/(lambda + 1) = ((-20)/3 + 2)/((-2)/3 + 1) = -14`,

`z = (lambda + 3)/(lambda + 1) = ((-2)/3 + 3)/((-2)/3 + 1) = 7`