1. 1) Sketch the region bounded by the polar curve r = −4cosθ and .
2) Find the area of the above region.
In exercise 2-3, find the length of the polar curves.
2. √
r = θ2 0 ≤ θ ≤ 5
3.
r = 2+2cos(θ) 0 ≤ θ ≤ π
4. Graph the points in the xyz-coordinate system satisfying the the given equations or inequalities.
1) x2 +y2 = 4 and z = −2.
2) x2 +y2 +z2 = 3 and z = 1.
5. Find the component form and length of the vector with initial point P (1,−2,3) and terminal point Q(−5,2,2).
6. Give u~ = h3,−2,1i, v~ = h2,−4,−3i, w~ = h−1,2,2i, find the magnitude of
(1) u~ +v~ +w~;
(2) 2u~ −3v~ −5w~.
7. Find a unit vector parallel to the sum of u~ = 2~i +4~j −5~k and v~ =~i +2~j +3~k.
8. Determine the value of x so that u~ = h2,x,1i and v~ = h4,−2,−2i are perpendicular.
