math

1. (9 points) Consider two lines: 1(t) = 1 + t, 23t, 2t1 and 2(t) = t, 1 + 3t, 25t.
(a) (4 points) Are the two lines parallel?
(b) (5 points) Do the two lines intersect? If so, find an intersection point. In any case
(whether they intersect or not), explain your answer.
2. (9 points) Let u and v be two vectors in R2such that u = 1, 1, v = 3, and uv = 1.
(a) (3 points) Find vu, the projection of v along u.
(b) (6 points) Find a number c such that 4u + cv and u v are orthogonal.
3. (12 points) Consider two planes 3x y z = 1 and x + 2y 3z = 0.
(a) (2 points) Write down a normal vector for each plane. Specify which vector corresponds
to which plane.
(b) (3 points) Write down a point (with the x, y, z-coordinates) that lies in the intersection
of the two planes.
(c) (7 points) Find a parametric equation for the line of the intersection of the two planes?