91Ó°ÊÓ

Find (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) \(\mathbf{u} \cdot(\mathbf{2 v})\) $$ \mathbf{u}=\langle 2,-3,4\rangle, \quad \mathbf{v}=\langle 0,6,5\rangle $$

Find the vectors \(u\) and \(v\) whose initial and terminal points are given. Show that \(\mathrm{u}\) and \(\mathrm{v}\) are equivalent. $$ \begin{aligned} &\text { u: }(3,2),(5,6) \\ &\text { v: }(-1,4),(1,8) \end{aligned} $$

Find the cross product of the unit vectors and \(A\) sketch vour result. $$ \mathbf{i} \times \mathbf{k} $$

Find sets of (a) parametric equations and (b) symmetric equations of the line through the point parallel to the given vector or line. (For each line, write the direction numbers as integers.)\((-2,0,3) \quad \mathbf{v}=2 \mathbf{i}+4 \mathbf{j}-2 \mathbf{k}\)

Convert the point from cylindrical coordinates to rectangular coordinates. \((4,7 \pi / 6,3)\)

Find sets of (a) parametric equations and (b) symmetric equations of the line through the point parallel to the given vector or line. (For each line, write the direction numbers as integers.)\((-3,0,2) \quad \mathbf{v}=6 \mathbf{j}+3 \mathbf{k}\)

Find (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) \(\mathbf{u} \cdot(\mathbf{2 v})\) $$ \mathbf{u}=\mathbf{i}, \quad \mathbf{v}=\mathbf{i} $$

Convert the point from cylindrical coordinates to rectangular coordinates. \((1,3 \pi / 2,1)\)

Find the cross product of the unit vectors and \(A\) sketch vour result. $$ \mathbf{k} \times \mathbf{i} $$

Find the vectors \(u\) and \(v\) whose initial and terminal points are given. Show that \(\mathrm{u}\) and \(\mathrm{v}\) are equivalent. $$ \begin{aligned} &\text { u: }(-4,0),(1,8)\\\ &\mathbf{v}:(2,-1),(7,7) \end{aligned} $$