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.

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