HW 6, MA 1023
1. 1) Sketch the region bounded by the polar curve r = −4cosθ and 3π
4
≤ θ ≤
5π
4
.
2) Find the area of the above region.
In exercise 2-3, find the length of the polar curves.
2.
r = θ
2
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) x
2 + y
2 = 4 and z = −2.
2) x
2 + y
2 + z
2 = 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) 2~u − 3~v − 5~w.
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.
