1. Let l1 be the line determined by (2,1, 3) and (1, 2 - 1) and let l2 be the line determined by (0, 2, 3) and (-1,1, 2) . Is l1 parallel to l2 ? Explain your answer.
2. Prove that for any two vectors u and v in R2 or R3 , u + v 2 + u - v 2 = 2 u 2 + 2 v 2 .
3. Find the parametric equations of the line through the origin that is perpendicular to both u=(-1,2,3) and v=(2,0,1/2).
4. Find the distance from the point P(1,-1,1) to the line x(t) = (0,2,1) + t(1,1,1), and the closest point on the line to point P .
5. Showthatthethreeplanes x+y+z=2, -x-y+4z=3 and x+y+2z=3 intersectin a line, and find the equation of that line.