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UNIQNESS

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Here are the problems I need help on:

1) Let r0 = <x0, y0, z0> and r = <x,y,z>. Describe the set of all points (x,y,z) for which

a) r dot r0 = 0.

b) (r - r0) dot r0 = 0

The 0 next to r, x, y, and z should be subscript.

2) Show that if u and v are vectors in 3-space, then |u x v|^2 = |u|^2 + |v|^2 - (u dot v)^2

(hint: use the pythagorean identity)

cos^2 theta + sin^2 theta = 1

3) Show that if u and v are unit vectors and theta is the angle between them, then |u - v| = 2 sin (1/2 theta)

Thanks in advance!