[SOLVED] MA1023 Homework 6

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.

• x² +y² = 4 and z = −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

• u~ +v~ +w~;
• 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.