91Ó°ÊÓ

Find the acute angles between the planes to the nearest hundredth of a radian. $$2 x+2 y-z=3, \quad x+2 y+z=2$$

Over the indicated domains. If you can, rotate the surface into different viewing positions. $$z=x^{2}+y^{2}, \quad-3 \leq x \leq 3, \quad-3 \leq y \leq 3$$

Find equations for the spheres whose centers and radii are given. Center (1,2,3) Radius \(\sqrt{14}\)

Over the indicated domains. If you can, rotate the surface into different viewing positions. $$z=x^{2}+2 y^{2} \text { over }$$ a. \(-3 \leq x \leq 3,-3 \leq y \leq 3\) b. \(-1 \leq x \leq 1,-2 \leq y \leq 3\) c. \(-2=x \leq 2,-2 \leq y \leq 2\) d. \(-2 \leq x \leq 2, \quad-1 \leq y \leq 1\)

Find the acute angles between the planes to the nearest hundredth of a radian. $$4 y+3 z=-12, \quad 3 x+2 y+6 z=6$$

Find equations for the spheres whose centers and radii are given. Center (0,-1,5) Radius 2

Find the vector from the origin to the point of intersection of the medians of the triangle whose vertices are $$ A(1,-1,2), \quad B(2,1,3), \quad \text { and } \quad C(-1,2,-1) $$

Let \(A B C D\) be a general, not necessarily planar, quadrilateral in space. Show that the two segments joining the midpoints of opposite sides of \(A B C D\) bisect each other. (Hint: Show that the segments have the same midpoint.)

Find the point in which the line meets the plane. $$x=1-t, \quad y=3 t, \quad z=1+t ; \quad 2 x-y+3 z=6$$

Find equations for the spheres whose centers and radii are given. Center \(\left(-1, \frac{1}{2},-\frac{2}{3}\right)\) Radius \(\frac{4}{9}\)