91Ó°ÊÓ

\(\begin{array}{ll}\text { } & \mathbf{}, & \text { describe } & \text { the family of planes }\end{array}\) represented by the equation, where \(c\) is any real number.\(c y+z=0\)

Use a computer algebra system or graphing utility to convert the point from one system to another among the rectangular, cylindrical, and spherical coordinate systems. \((3,-2,2)\)

Find the magnitude of \(\mathrm{v}\). \(\mathbf{v}=\langle 1,0,3\rangle\)

\(\begin{array}{ll}\text { } & \mathbf{}, & \text { describe } & \text { the family of planes }\end{array}\) represented by the equation, where \(c\) is any real number.\(x+c z=0\)

Use a computer algebra system or graphing utility to convert the point from one system to another among the rectangular, cylindrical, and spherical coordinate systems. \((3 \sqrt{2}, 3 \sqrt{2},-3)\)

(a) find the unit tangent vectors to each curve at their points of intersection and (b) find the angles \(\left(0 \leq \theta \leq 90^{\circ}\right)\) between the curves at their points of intersection. $$ y=x^{3}, \quad y=x^{1 / 3} $$

Use a computer algebra system or graphing utility to convert the point from one system to another among the rectangular, cylindrical, and spherical coordinate systems. \((5 / 2,4 / 3,-3 / 2)\)

(a) find the unit tangent vectors to each curve at their points of intersection and (b) find the angles \(\left(0 \leq \theta \leq 90^{\circ}\right)\) between the curves at their points of intersection. $$ y=1-x^{2}, \quad y=x^{2}-1 $$

Find the magnitude of \(\mathrm{v}\). \(\mathbf{v}=\mathbf{i}-2 \mathbf{j}-3 \mathbf{k}\)

In Exercises 81 and 82, find a set of parametric equations for the line of intersection of the planes. \(3 x+2 y-z=7\) \(x-4 y+2 z=0\)