91Ó°ÊÓ

In Exercises 24-27, find ${\mathrm{comp}}_{\mathbf{u}}\mathbf{v}\mathbf{},{\mathrm{proj}}_{\mathbf{u}}\mathbf{v}$ and the component of v orthogonal tou.

role="math" localid="1649693816584"

Find $u+vandu-v$also sketch $u,v,u+v,u-v$

role="math" localid="1649603034674" $u=\left(1,-4,6\right)andv=\left(2,-4,7\right)$

In Exercises 22–29 compute the indicated quantities when $u=(2,1,−3),v=(4,0,1),\mathrm{and}w=(−2,6,5)$

Find the area of the parallelogram determined by the vectors u and v.

In Exercises 28-31, find ${\mathrm{proj}}_{\mathbf{u}}\mathbf{v}\mathbf{}\mathrm{and}\mathbf{}{\mathrm{proj}}_{\mathbf{v}}\mathbf{u}$.

Find the equations of the planes determined by the given conditions.

The plane contains the point $(1,2,−5)$and the line determined

by$\mathbf{r}\left(t\right)=⟨3+7t,-2+t,3+4tâŸ\copyright$

Find $u+vandu-v$also sketch $u,v,u+v,u-v$

role="math" localid="1649603943715" $u=\left(3,6,11\right)andv=\left(1,-2,3\right)$

In Exercises 23–28, find an equation of the line containing the given point and parallel to the given vector. Express your answer (a) as a vector parametrization, (b) in terms of parametric equations, and (c) in symmetric form.

\(P\left ( 1,3,-2,4 \right ),d=\left<4,-1,5,8 \right>\)

Calculate the limits in Exercises $25-28$, using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.

localid="1648227587052" $\underset{x→0}{\lim }\frac{3}{2x^2-4x+1}$.

In Exercises 22–29 compute the indicated quantities when $u=(2,1,−3),v=(4,0,1),\mathrm{and}w=(−2,6,5)$

Find the area of the parallelogram determined by the vectors v and w.

Find the equation of sphere with center (3, -2, 5) and radius 5.