MATH 210 Study Guide - Final Guide: Dot Product, Cross Product, Unit Vector
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Solution: (a) the cosine of the angle between u and v is: cos = u v. Since the magnitudes of the vectors are positive, the sign of the dot product will determine whether the angle is acute, obtuse, or right. U v = h1, 1, 0i h2, 1, 3i = 1. N = [( 1)(3) (0)(1)] [(1)(3) (0)(2)] + k [(1)(1) ( 1)(2)] N = 3 3 + 3 k. Using (1, 1, 2) as a point on the plane, we have: 3(x 1) 3(y + 1) + 3(z 2) = 0. Solution: (a) the velocity and acceleration vectors are: V (t) = r (t) = h2 cos(t), 2 sin(t), 1i. A (t) = v (t) = h 2 sin(t), 2 cos(t), 0i (b) a vector equation for the line tangent to r (t) at t0 is: L (t) = r (t0) + r (t0)(t t0)
