Problem 5
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.) $$ (-2,0,3) \quad \mathbf{v}=2 \mathbf{i}+4 \mathbf{j}-2 \mathbf{k} $$
Problem 5
Find the area of the region. One petal of \(r=2 \cos 3 \theta\)
Problem 5
In Exercises \(1-8,\) describe and sketch the surface. $$ 4 x^{2}+y^{2}=4 $$
Problem 6
What is the \(x\) -coordinate of any point in the yz-plane?
Problem 6
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 \((e) u \cdot(2 v)\). $$ \begin{array}{l} \mathbf{u}=2 \mathbf{i}+\mathbf{j}-2 \mathbf{k} \\ \mathbf{v}=\mathbf{i}-3 \mathbf{j}+2 \mathbf{k} \end{array} $$
Problem 6
Find the cross product of the unit vectors and sketch your result. $$ \mathbf{k} \times \mathbf{i} $$
Problem 6
In Exercises \(5-8,\) convert the point from rectangular coordinates to cylindrical coordinates. $$ (2 \sqrt{2},-2 \sqrt{2}, 4) $$
Problem 6
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.) $$ (-3,0,2) \quad \mathbf{v}=6 \mathbf{j}+3 \mathbf{k} $$
Problem 6
In Exercises \(1-8,\) describe and sketch the surface. $$ y^{2}-z^{2}=4 $$
Problem 6
Find the area of the region. One petal of \(r=6 \sin 2 \theta\)
