Question

The point in which the join of (–9, 4, 5) and (11, 0, –1) is met by the perpendicular from the origin is ______.

Options

• (2, 1, 2)

• (2, 2, 1)

• (1, 2, 2)

• (1, 1, 2)

Answer 1

The point in which the join of (–9, 4, 5) and (11, 0, –1) is met by the perpendicular from the origin is (1, 2, 2).

Explanation:

Direction ratios of the line joining the points (–9, 4, 5) and (11, 0, –1) is = (20, –4, –6)

It is passing through (–9, 4, 5)

It's equation is `(x + 9)/20 = (y - 4)/(-4) = (z - 5)/(-6)` = r

Let any point on this line is given as (20r – 9, –4r + 4, –6r + 5)  ....(i)

Direction ratios of the line passing through origin and point (i) we have (20r – 9, –4r + 4, 6r + 5)

It is perpendicular with (20, –4, –6)

⇒ 20(20r – 9) – 4(4r + 4) – 6(6r + 5) = 0

⇒ r = `1/2`

Point is (1, 2, 2)