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Chapter 6: Problem 9
Plot each complex number and find its absolute value. $$z=-3+4 i$$
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Help you prepare for the material covered in the first section of the next chapter. a. Does (4,-1) satisfy \(x+2 y=2 ?\) b. Does (4,-1) satisfy \(x-2 y=6 ?\)
Find \(\text {pro}_{\mathbf{w}} \mathbf{V}\) Then decompose v into two vectors, \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2},\) where \(\mathbf{v}_{1}\) is parallel to \(\mathbf{w}\) and \(\mathbf{v}_{2}\) is orthogonal to \(\mathbf{w}.\) $$\mathbf{v}=2 \mathbf{i}+4 \mathbf{j}, \quad \mathbf{w}=-3 \mathbf{i}+6 \mathbf{j}$$
Let $$\mathbf{u}=-\mathbf{i}+\mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}-2 \mathbf{j}, \quad \text { and } \quad \mathbf{w}=-5 \mathbf{j}$$ Find each specified scalar or vector. $$\operatorname{proj}_{\mathbf{u}}(\mathbf{v}-\mathbf{w})$$
Use the dot product to determine whether v and w are orthogonal. $$\mathbf{v}=2 \mathbf{i}+8 \mathbf{j}, \quad \mathbf{w}=4 \mathbf{i}-\mathbf{j}$$
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.
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