Chapter 9: Problem 40
What is meant by the trace of a surface? How do you find a trace?
Chapter 9: Problem 40
What is meant by the trace of a surface? How do you find a trace?
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Get started for free(a) find the unit tangent vectors to each curve at their points of intersection and (b) find the angles \(\left(0 \leq \theta \leq 90^{\circ}\right)\) between the curves at their points of intersection. $$ y=x^{3}, \quad y=x^{1 / 3} $$
Writing The initial and terminal points of the vector \(\mathbf{v}\) are \(\left(x_{1}, y_{1}, z_{1}\right)\) and \((x, y, z) .\) Describe the set of all points \((x, y, z)\) such that \(\|\mathbf{v}\|=4\)
Prove the Cauchy-Schwarz Inequality \(|\mathbf{u} \cdot \mathbf{v}| \leq\|\mathbf{u}\|\|\mathbf{v}\| .\)
Find \(u \cdot v\). \(\|\mathbf{u}\|=40,\|\mathbf{v}\|=25,\) and the angle between \(\mathbf{u}\) and \(\mathbf{v}\) is \(5 \pi / 6\).
Use vectors to prove that a parallelogram is a rectangle if and only if its diagonals are equal in length.
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