Question

The shortest distance between A (1, 0, 2) and the line `(x + 1)/3 = (y - 2)/(-2) = (z + 1)/(-1)` is given by line joining A and B, then B in the line is ______ 

पर्याय

• `(1/2, 1, (-3)/2)`

• `(2/3, 1, -1)`

• `(2/3, (-1)/2, -2)`

• (1, -2, -1)

Answer 1

The shortest distance between A (1, 0, 2) and the line `(x + 1)/3 = (y - 2)/(-2) = (z + 1)/(-1)` is given by line joining A and B, then B in the line is `underline((1/2, 1, (-3)/2))`.

Explanation:

Let `(x + 1)/3 = (y - 2)/(-2) = (z + 1)/(-1) = lambda`

Any general point on this line is

B (3λ - 1, -2λ + 2, -λ - 1)

Let A ≡ (1, 0, 2)

∴ d.r.s. of AB are 3λ - 2, -2λ + 2, -λ - 3

Since, AB is perpendicular to the given line,

∴ 3(3λ - 2) - 2(-2λ + 2) - 1(-λ - 3) = 0

⇒ 14λ = 7

⇒ λ = `1/2`

∴ B ≡ `(1/2, 1, (-3)/2)`