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Chapter 6: Problem 92
What is the vector \(\mathbf{j} ?\)
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A force of 6 pounds acts in the direction of \(40^{\circ}\) to the horizontal. The force moves an object along a straight line from the point (5,9) to the point \((8,20),\) with the distance measured in feet. Find the work done by the force.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. There are no points on my graph of \(r^{2}=9 \cos 2 \theta\) for which \(\frac{\pi}{4}<\theta<\frac{3 \pi}{4}\)
Use the dot product to determine whether v and w are orthogonal. $$\mathbf{v}=5 \mathbf{i}-5 \mathbf{j}, \quad \mathbf{w}=\mathbf{i}-\mathbf{j}$$
Exercises \(81-83\) will help you prepare for the material covered in the next section. Find the obtuse angle \(B,\) rounded to the nearest degree, satisfying $$ \cos B=\frac{6^{2}+4^{2}-9^{2}}{2 \cdot 6 \cdot 4} $$
Find the angle, in degrees, between \(\mathbf{v}\) and \(\mathbf{w}.\) $$\mathbf{v}=2 \cos \frac{4 \pi}{3} \mathbf{i}+2 \sin \frac{4 \pi}{3} \mathbf{j}, \quad \mathbf{w}=3 \cos \frac{3 \pi}{2} \mathbf{i}+3 \sin \frac{3 \pi}{2} \mathbf{j}$$
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