Find the vector and cartesian equation of a line through the point (1, -1, 1) and perpendicular to the lines joining the points (4, 3, 2), (1,-1,0) and (1, 2, -1), (2, 1, 1).

Answer

`(x-1)/(10) = (y+1)/(-4) = (z-1)/(-7)`; its corresponding vector equation is `r = (hat(i) - hat(j) + hat(k)) + lambda(10 hat(i) - 4hat(j) - 7 hat(k))`