1. Show that given any four vectors r, u, v, w in R 3 , then there are four scalars a, b, c, and d such that ar + bu + cv + dw = 0.

2. Show that the three points (1, 2, 3),(1, 0, 4), and (0, 2, 3) form a triangle and find the area of that triangle.

3. Given two vectors u, w and a scalar k, characterize any vector v that satisfies uv = w and u v = k.

4. Show that the two lines given explicitly by the position vector equations hx, y, zi = ht, 1 t, 4t 8i and hx, y, zi = h2s + 2, 2s 1, 3si intersect. Find an equation of a line through that intersection point which is perpendicular to both lines