?[T] Assume that the magnitudes of two nonzero vectors u and v are known. The function

Chapter 2, Problem 232

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[T] Assume that the magnitudes of two nonzero vectors u and v are known. The function \(f(\theta)=\|\mathbf{u}\| \quad\|\mathbf{v}\| \sin \theta\) defines the magnitude of the cross product vector \(\mathbf{u} \times \mathbf{v}\), where \(\theta \in[0, \pi]\) is the angle between u and v.

a. Graph the function f.

b. Find the absolute minimum and maximum of function f. Interpret the results.

c. If \(\|\mathbf{u}\|=5\) and \(\|\mathbf{v}\|=2\), find the angle between u and v if the magnitude of their cross product vector is equal to 9.

Text Transcription:

f(theta) = |u| |v| sin theta

u times v

theta [0, pi]

|u| = 5

|v| = 2