Problem 7
Find \((a) \mathbf{u} \times \mathbf{v},(b) \mathbf{v} \times \mathbf{u},\) and \((\mathbf{c}) \mathbf{v} \times \mathbf{v}\). $$ \begin{array}{l} \mathbf{u}=-2 \mathbf{i}+3 \mathbf{j}+4 \mathbf{k} \\ \mathbf{v}=3 \mathbf{i}+7 \mathbf{j}+2 \mathbf{k} \end{array} $$
Problem 7
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.) $$ (1,0,1) \quad x=3+3 t, y=5-2 t, z=-7+t $$
Problem 7
In Exercises \(1-8,\) describe and sketch the surface. $$ z-\sin y=0 $$
Problem 7
In Exercises \(5-8,\) convert the point from rectangular coordinates to cylindrical coordinates. $$ (2,-2,-4) $$
Problem 7
Find the area of the region. One petal of \(r=\cos 2 \theta\)
Problem 7
In Exercises 7 and \(8,\) find \(u \cdot v\). \(\|\mathbf{u}\|=8,\|\mathbf{v}\|=5,\) and the angle between \(\mathbf{u}\) and \(\mathbf{v}\) is \(\pi / 3\).
Problem 7
In Exercises \(7-18,\) determine the location of a point \((x, y, z)\) that satisfies the condition(s). \(z=6\)
Problem 8
Find \((a) \mathbf{u} \times \mathbf{v},(b) \mathbf{v} \times \mathbf{u},\) and \((\mathbf{c}) \mathbf{v} \times \mathbf{v}\). $$ \begin{array}{l} \mathbf{u}=3 \mathbf{i}+5 \mathbf{k} \\ \mathbf{v}=2 \mathbf{i}+3 \mathbf{j}-2 \mathbf{k} \end{array} $$
Problem 8
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.) $$ (-3,5,4) \quad \frac{x-1}{3}=\frac{y+1}{-2}=z-3 $$
Problem 8
Find \(u \cdot v\). \(\|\mathbf{u}\|=40,\|\mathbf{v}\|=25,\) and the angle between \(\mathbf{u}\) and \(\mathbf{v}\) is \(5 \pi / 6\).
