Question

The line which passes through the origin and intersect the two lines `(x - 1)/2 = (y + 3)/4 = (z - 5)/3, (x - 4)/2 = (y + 3)/3 = (z - 14)/4`, is ______.

Options

• `x/1 = y/(-3) = z/5`

• `x/(-1) = y/3 = z/5`

• `x/1 = y/3 = z/(-5)`

• `x/1 = y/4 = z/(-5)`

Answer 1

The line which passes through the origin and intersect the two lines `(x - 1)/2 = (y + 3)/4 = (z - 5)/3, (x - 4)/2 = (y + 3)/3 = (z - 14)/4`, is `underlinebb(x/1 = y/(-3) = z/5)`.

Explanation:

Let the line be `x/a = y/b = z/c`  ...(i)

If line (i) intersects with the line `(x - 1)/2`

= `(y + 3)/4 = (z - 5)/3`, then

`|(a, b, c),(2, 4, 3),(4, -3, 14)|` = 0 `\implies` 9a – 7b – 10c = 0  ...(ii)

From (i) and (ii), we have `a/1 = b/(-3) = c/5`

∴ The line is `x/1 = y/(-3) = z/5`