Download Review Quiz 6.1, 6.3 Solutions

Review for Quiz 6.1, 6.3
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For 1-3, let u = <2, -1>, v = <4, 2>, and w = <1, -3>. Find:
1. u + v
2. v – w
3. 2u + v - 3w
4. Find the component form of a vector AB with A = (2, -1) and B = (3, 1).
5. Find the magnitude and direction angle of the vector in #4.
6. Find the component form of a vector with a direction angle of 127 degrees and magnitude of 28.
7. An airplane flies at a bearing of 305 degrees and at a speed of 480 miles per hour. Find the
component form of the velocity vector of the plane.
For 8-9, eliminate the parameter and identify the type of graph it is.
8. x = 3 – 5t, y = 4 + 3t
9. x = 3cost, y = 3sint
For 10-12, find a parametrization for each.
10. The line through points (-1, -2) and (3, 4).
11. The line segment through points (-2, 3) and (5, 1).
12. A circle with radius of 6 and center at (4, 5).
13. Stewart shoots an arrow straight up from the top of a building with initial velocity of 245 ft/sec.
The arrow leaves from a point 200 feet above the ground.
a) Write a parametric equation to model the height of the arrow. (Make X = some #)
b) How high is the arrow after 4 seconds? (Use the table.)
c) What is the maximum height of the arrow? When does it reach that height?
d) When will the arrow hit the ground?
14. Spencer practices kicking field goals 40 yards from a goal post with a crossbar that is 10 feet high.
If he kicks the ball with an initial velocity of 60 feet per second at a 47 degree angle with the ground,
will he make a field goal (clear the cross bar)? (Write parametric equations and use your calculator to
graph. Justify your answer with the numbers from the table that made you believe that he would or
would not make the field goal.)
Football:
Cross Bar:
X = ____________________________
X = ____________________________
Y = ____________________________
Y = ____________________________
Justification: