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Chapter 11: Problem 11
Performing Vector Operations In Exercises \(5-14\) use the vectors \(u=3 i-j+4 k\) and \(v=2 i+2 j-k\) to find the expression. $$(-2 \mathbf{u}) \times \mathbf{v}$$
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Finding the Area of a Parallelogram In Exercises \(37-44,\) find the area of the parallelogram that has the vectors as adjacent sides. $$\mathbf{u}=-2 \mathbf{i}+3 \mathbf{j}+2 \mathbf{k}$$ $$\mathbf{v}=\mathbf{i}+2 \mathbf{j}+4 \mathbf{k}$$
True or False?, determine whether the statement is true or false. Justify your answer. $$\begin{array}{l}{\text { If } A B \text { and } A C \text { are parallel vectors, then points } A, B, \text { and }} \\ {C \text { are collinear. }}\end{array}$$
Finding the Cross Product In Exercises \(15-28\) , find \(\mathbf{u} \times \mathbf{v}\) and show that it is orthogonal to both \(\mathbf{u}\) and \(\mathbf{v} .\) $$\begin{aligned} \mathbf{u} &=2 \mathbf{i}+4 \mathbf{j}+3 \mathbf{k} \\\ \mathbf{v} &=-\mathbf{i}+3 \mathbf{j}-2 \mathbf{k} \end{aligned}$$
Performing Vector Operations In Exercises \(5-14\) use the vectors \(u=3 i-j+4 k\) and \(v=2 i+2 j-k\) to find the expression. $$\mathbf{u} \times(2 \mathbf{v})$$
Graphing a Sphere In Exercises \(75-78,\) use a three-dimensional graphing utility to graph the sphere. $$x^{2}+y^{2}+z^{2}-6 x-8 y-10 z+46=0$$
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