Chapter 9: Problem 70
Label any intercepts and sketch a graph of the plane. $$ z=8 $$
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Prove the Cauchy-Schwarz Inequality \(|\mathbf{u} \cdot \mathbf{v}| \leq\|\mathbf{u}\|\|\mathbf{v}\| .\)
Find each scalar multiple of \(v\) and sketch its graph. \(\mathbf{v}=\langle 2,-2,1\rangle\) (a) - \(\mathbf{v}\) (b) \(2 \mathbf{v}\) (c) \(\frac{1}{2} \mathbf{v}\) (d) \(\frac{5}{2} \mathbf{v}\)
Find the vector \(z,\) given that \(\mathbf{u}=\langle 1,2,3\rangle\) \(\mathbf{v}=\langle 2,2,-1\rangle,\) and \(\mathbf{w}=\langle 4,0,-4\rangle\) \(\mathbf{z}=5 \mathbf{u}-3 \mathbf{v}-\frac{1}{2} \mathbf{w}\)
In Exercises \(65-68,\) find the magnitude of \(v\). \(\mathbf{v}=\mathbf{i}-2 \mathbf{j}-3 \mathbf{k}\)
The initial and terminal points of a vector \(v\) are given. (a) Sketch the directed line segment, (b) find the component form of the vector, and (c) sketch the vector with its initial point at the origin. Initial point: (2,-1,-2) Terminal point: (-4,3,7)
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