91Ó°ÊÓ

Using the Cross Product In Exercises \(29-36,\) find a unit vector that is orthogonal to both \(u\) and v. $$\mathbf{u}=3 \mathbf{i}+\mathbf{j}$$ $$\mathbf{v}=\mathbf{j}+\mathbf{k}$$

Using the Cross Product In Exercises \(29-36,\) find a unit vector that is orthogonal to both \(u\) and v. $$\mathbf{u}=\mathbf{i}+2 \mathbf{j}$$ $$\mathbf{v}=\mathbf{i}-3 \mathbf{k}$$

Finding the Magnitude of a Vector ,find the magnitude of \(v\) . $$\mathbf{v}=2 \mathbf{i}-\mathbf{j}+6 \mathbf{k}$$

Finding the Distance Between Two Points in Space In Exercises \(27-36,\) tind the distance between the points. $$(1,1,-7),(-2,-3,-7)$$

Using the Cross Product In Exercises \(29-36,\) find a unit vector that is orthogonal to both \(u\) and v. $$\mathbf{u}=-3 \mathbf{i}+2 \mathbf{j}-5 \mathbf{k}$$ $$\mathbf{v}=\frac{1}{2} \mathbf{i}-\frac{3}{4} \mathbf{j}+\frac{1}{10} \mathbf{k}$$

Initial point: \((1,-3,4) ;\) terminal point: \((1,0,-1)\)

Finding the Distance Between Two Points in Space In Exercises \(27-36,\) tind the distance between the points. $$(0,-3,0),(1,0,-10)$$

Finding an Equation of a Plane in Three-Space In Exercises \(31 - 36\) , find the general form of the equation of the plane with the given characteristics. $$ \begin{array} { l } { \text { Passes through } ( 0,2,4 ) \text { and } ( - 1 , - 2,0 ) \text { and is } } \\ { \text { perpendicular to the } y z \text { -plane } } \end{array} $$

Using the Cross Product In Exercises \(29-36,\) find a unit vector that is orthogonal to both \(u\) and v. $$\mathbf{u}=7 \mathbf{i}-14 \mathbf{j}+5 \mathbf{k}$$ $$\mathbf{v}=14 \mathbf{i}+28 \mathbf{j}-15 \mathbf{k}$$

Finding the Distance Between Two Points in Space In Exercises \(27-36,\) tind the distance between the points. $$(2,-4,0),(0,6,-3)$$