Problem 4
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 \((e) u \cdot(2 v)\). $$ \mathbf{u}=\mathbf{i}, \quad \mathbf{v}=\mathbf{i} $$
Problem 4
Find the cross product of the unit vectors and sketch your result. $$ \mathbf{k} \times \mathbf{j} $$
Problem 4
In Exercises \(1-8,\) describe and sketch the surface. $$ y^{2}+z=4 $$
Problem 4
In Exercises \(1-4,\) convert the point from cylindrical coordinates to rectangular coordinates. $$ (6,-\pi / 4,2) $$
Problem 4
Find the area of the region bounded by the graph of the polar equation using (a) a geometric formula and (b) integration. $$ r=3 \cos \theta $$
Problem 4
Find the coordinates of the point. The point is located in the \(y z\) -plane, three units to the right of the \(x z\) -plane, and two units above the \(x y\) -plane.
Problem 5
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 \((e) u \cdot(2 v)\). $$ \begin{array}{l} \mathbf{u}=2 \mathbf{i}-\mathbf{j}+\mathbf{k} \\ \mathbf{v}=\mathbf{i}-\mathbf{k} \end{array} $$
Problem 5
Find the cross product of the unit vectors and sketch your result. $$ \mathbf{i} \times \mathbf{k} $$
Problem 5
Find the area of the region. One petal of \(r=2 \cos 3 \theta\)
Problem 5
What is the \(z\) -coordinate of any point in the \(x y\) -plane?
