91Ó°ÊÓ

Finding Equations In Exercises \(11 - 18 ,\) find (a) a set of parametric equations and (b) if possible, a set of symmetric equations of the line that passes through the points. (Write the direction numbers as integers.) $$ ( 2,3,0 ) , ( 10,8,12 ) $$

Plotting Points in Space In Exercises \(9-14,\) plot both points in the same three-dimensional coordinate system. $$\begin{array}{l}{\text { (a) }(0,4,-3)} \\ {\text { (b) }(4,0,4)}\end{array}$$

Performing Vector Operations In Exercises \(5-14\) use the vectors \(u=3 i-j+4 k\) and \(v=2 i+2 j-k\) to find the expression. $$\mathbf{u} \cdot(\mathbf{u} \times \mathbf{v})$$

Finding Equations In Exercises \(11 - 18 ,\) find (a) a set of parametric equations and (b) if possible, a set of symmetric equations of the line that passes through the points. (Write the direction numbers as integers.) $$ ( - 3,8,15 ) , ( 1 , - 2,16 ) $$

Finding the Component Form of a Vector, find the component form of the vector v. $$\begin{array}{ll}{\text { Initial point }} & {\text { Terminal point }} \\\ {(-1,2,-4)} & {(1,4,-4)}\end{array}$$

Plotting Points in Space In Exercises \(9-14,\) plot both points in the same three-dimensional coordinate system. $$\begin{array}{l}{\text { (a) }(3,-2,5)} \\ {\text { (b) }\left(\frac{3}{2}, 4,-2\right)}\end{array}$$

Finding Equations In Exercises \(11 - 18 ,\) find (a) a set of parametric equations and (b) if possible, a set of symmetric equations of the line that passes through the points. (Write the direction numbers as integers.) $$ ( 2,3 , - 1 ) , ( 1 , - 5,3 ) $$

Finding the Component Form of a Vector, find the component form of the vector v. $$\begin{array}{ll}{\text { Initial point }} & {\text { Terminal point }} \\\ {(0,-1,0)} & {(0,2,1)}\end{array}$$

Performing Vector Operations In Exercises \(5-14\) use the vectors \(u=3 i-j+4 k\) and \(v=2 i+2 j-k\) to find the expression. $$\mathbf{v} \cdot(\mathbf{v} \times \mathbf{u})$$

Plotting Points in Space In Exercises \(9-14,\) plot both points in the same three-dimensional coordinate system. $$\begin{array}{l}{\text { (a) }(5,-2,2)} \\ {\text { (b) }(5,-2,-2)}\end{array}$$