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?
All the tools & learning materials you need for study success - in one app.
Get started for freeIf the projection of \(\mathbf{u}\) onto \(\mathbf{v}\) has the same magnitude as the projection of \(\mathbf{v}\) onto \(\mathbf{u}\), can you conclude that \(\|\mathbf{u}\|=\|\mathbf{v}\|\) ? Explain.
Find \((\mathbf{a}) \mathbf{u} \cdot \mathbf{v},(\mathbf{b}) \mathbf{u} \cdot \mathbf{u},(\mathbf{c})\|\mathbf{u}\|^{2},(\mathbf{d})(\mathbf{u} \cdot \mathbf{v}) \mathbf{v}\) and \((e) u \cdot(2 v)\). $$ \mathbf{u}=\mathbf{i}, \quad \mathbf{v}=\mathbf{i} $$
Consider a regular tetrahedron with vertices \((0,0,0),(k, k, 0),(k, 0, k),\) and \((0, k, k),\) where \(k\) is a positive real number. (a) Sketch the graph of the tetrahedron. (b) Find the length of each edge. (c) Find the angle between any two edges. (d) Find the angle between the line segments from the centroid \((k / 2, k / 2, k / 2)\) to two vertices. This is the bond angle for a molecule such as \(\mathrm{CH}_{4}\) or \(\mathrm{PbCl}_{4}\), where the structure of the molecule is a tetrahedron.
Find the magnitude of \(v\). \(\mathbf{v}=\langle 1,0,3\rangle\)
Find the vector \(z,\) given that \(\mathbf{u}=\langle 1,2,3\rangle\) \(\mathbf{v}=\langle 2,2,-1\rangle,\) and \(\mathbf{w}=\langle 4,0,-4\rangle\) \(2 \mathbf{z}-3 \mathbf{u}=\mathbf{w}\)
What do you think about this solution?
We value your feedback to improve our textbook solutions.