91Ó°ÊÓ

The line passes through the point \((-4,5,2)\) and is perpendicular to the plane given by \(-x+2 y+z=5\).

Describe and sketch the surface. $$ z-e^{y}=0 $$

The initial and terminal points of a vector \(\mathbf{v}\) are given. (a) Sketch the given directed line segment, (b) write the vector in component form, and (c) sketch the vector with its initial point at the origin. $$ (0.12,0.60) \quad(0.84,1.25) $$

Find the angle \(\theta\) between the vectors. $$ \begin{aligned} &\mathbf{u}=3 \mathbf{i}+2 \mathbf{j}+\mathbf{k} \\ &\mathbf{v}=2 \mathbf{i}-3 \mathbf{j} \end{aligned} $$

Sketch each scalar multiple of \(\mathbf{v}\). \(\mathbf{v}=\langle 2,3\rangle\) (a) \(2 \mathbf{v}\) (b) \(-3 \mathbf{v}\) (c) \(\frac{7}{2} v\) (d) \(\frac{2}{3} \mathbf{v}\)

The line passes through the point \((5,-3,-4)\) and is parallel to \(\mathbf{v}=\langle 2,-1,3\rangle\)

Determine the location of a point \((x, y, z)\) that satisfies the condition(s). \(y<0\)

Find the angle \(\theta\) between the vectors. $$ \begin{aligned} &\mathbf{u}=3 \mathbf{i}+4 \mathbf{j} \\ &\mathbf{v}=-2 \mathbf{j}+3 \mathbf{k} \end{aligned} $$

The line passes through the point \((-1,4,-3)\) and is parallel to \(\mathbf{v}=5 \mathbf{i}-\mathbf{j}\)

Find the angle \(\theta\) between the vectors. $$ \begin{aligned} &\mathbf{u}=2 \mathbf{i}-3 \mathbf{j}+\mathbf{k} \\ &\mathbf{v}=\mathbf{i}-2 \mathbf{j}+\mathbf{k} \end{aligned} $$