91Ó°ÊÓ

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. $$(3 \mathbf{u}) \times \mathbf{v}$$

Finding Equations In Exercises \(5 - 10\) , find (a) a set of parametric equations and (b) if possible, a set of symmetric equations of the line passing through the point and parallel to the specified vector or line. (Write the direction numbers as integers.) $$ ( 1,0,1 ) \quad x = 3 + 3 t , y = 5 - 2 t , z = - 7 + t $$

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. $$\mathbf{u} \times(2 \mathbf{v})$$

Plotting Points in Space In Exercises \(9-14,\) plot both points in the same three-dimensional coordinate system. $$\begin{array}{l}{\text { (a) }(3,0,0)} \\ {\text { (b) }(-3,-2,-1)}\end{array}$$

Plotting Points in Space In Exercises \(9-14,\) plot both points in the same three-dimensional coordinate system. $$\begin{array}{l}{\text { (a) }(3,-1,0)} \\ {\text { (b) }(-4,2,2)}\end{array}$$

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.) $$ ( 2,0,2 ) , ( 1,4 , - 3 ) $$

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. $$(-2 \mathbf{u}) \times \mathbf{v}$$

Finding the Component Form of a Vector, find the component form of the vector v. $$\begin{array}{ll}{\text { Initial point }} & {\text { Terminal point }} \\\ {(-6,4,-2)} & {(1,-1,3)}\end{array}$$

Finding the Component Form of a Vector, find the component form of the vector v. $$\begin{array}{ll}{\text { Initial point }} & {\text { Terminal point }} \\\ {(-7,3,-5)} & {(0,0,2)}\end{array}$$

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