The vector of real numbers U = 3u1 u2 4 can be visualized
Chapter 5, Problem 20(choose chapter or problem)
The vector of real numbers U = 3u1 u2 4 can be visualized on the real-number plane as an arrow from the origin to the point (u1, u2). The length of the arrow, also called the magnitude of the vector, is given by 0 0U 0 0 = "u2 1 + u2 2. The dot product of two such vectors, U v, is defined to be the real number u1v1 + u2v2. Show that if u is the angle between U and v, 0 u p, then cosu = U v 0 0U 0 0 # 0 0v 0 0 (Hint: Use the law of cosines.)
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