Question

Find the equation of the line which passes through the point (-1,2,3) and is perpendicular to the lines (x/2) = (y - 1)/-3 = (z + 2)/-2 and (x + 3)/-1 = (y + 2)/2 = (z - 1)/3.

Answer 1

Let direction ratio's of the required line be a, b, c since it is perpendicular to the two given lines 

2a - 3b - 2c = 0 ...(i)

and -a + 2b + 3c = 0 ...(ii)

Solving (i) and (ii) by cons multiplication,let us

a/-5 = b/-4 = c/1 = k (let)

Thus the required line passes through (-1,2,3) and has direction ratio propersonal to -5, 4, 1. so it eqn. in

(x + 1)/-5 = (y - 2)/-4 = (x - 3)/1