Question

If `(x - 1)/l = (y - 2)/m = (z + 1)/n` is the equation of the line through (1, 2, -1) and (-1, 0, 1), then (l, m, n) is ______ 

विकल्प

• (-1, 0, 1)

• (1, 1, -1)

• (1, 2, -1)

• (0, 1, 0)

Answer 1

If `(x - 1)/l = (y - 2)/m = (z + 1)/n` is the equation of the line through (1, 2, -1) and (-1, 0, 1), then (l, m, n) is (1, 1, -1).

Explanation:

Given equation is `(x - 1)/l = (y - 2)/m = (z + 1)/n`

The equation of line passing through (1, 2, -1) and (-1, 0, 1) is 

`(x - 1)/(-1 - 1) = (y - 2)/(0 - 2) = (z + 1)/(1 + 1)`

⇒ `(x - 1)/(-2) = (y - 2)/(-2) = (z + 1)/(2)`

⇒ `(x - 1)/1 = (y - 2)/1 = (z + 1)/(-1)` ..............(i)

Comparing (i) with given equation, we get

l = 1, m = 1, n = -1