Question

A line passes through (2, - 1, 3) and is perpendicular to the lines

vector r = (i + j - k) + λ(2i - 2j + k)

and vector r = (2i - j -3k) + μ(i + 2j +2k).

Obtain its equation in vector and cartesian form.

Answer 1

The direction perpendicular to the given lines is given by (2i - 2j + k) x ( i + 2j + 2k)

and the cartesian form is

x-2/2 = y+1/1 = z-3/-2.