Pre Calculus Exam Review Vectors_With Answers.pdf
Pre Calculus Exam Review Vectors_With Answers.pdf
Pre Calculus Exam Review Vectors_With Answers.pdf
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<strong>Pre</strong> <strong>Calculus</strong> <strong>Exam</strong> <strong>Review</strong> <strong>Vectors</strong>_<strong>With</strong> <strong>Answers</strong> on 3-4-2011<br />
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.<br />
Solve the problem.<br />
1) Let vector u have initial point P1 = (0, 2) and terminal point P2 = (3, -2). Let vector v have initial point<br />
Q1 = (3, 0) and terminal point Q2 = (6, -4). u and v have the same direction. Find u and v . Is u = v<br />
Answer:<br />
u = 5, v = 5; yes<br />
Find the magnitude v of the vector.<br />
2) v = 9i + 12j<br />
Answer: 15<br />
3) v = -i - j<br />
Answer: 2<br />
A vector v has initial point P1 and terminal point P2. Write v in terms of ai + bj.<br />
4) P1 = (-2, 3); P2 = (-5, -6)<br />
Answer: v = -3i - 9j<br />
Find the specified vector or scalar.<br />
5) v = 3i + 4j; Find 2v.<br />
Answer: 6i + 8j<br />
Find the unit vector having the same direction as v.<br />
6) v = -3i - 4j<br />
Answer: u = - 3 5 i - 4 5 j<br />
Write a vector v in terms of i and j whose magnitude v and direction angle θ are given.<br />
7) v = 10, θ = 120°<br />
Answer: v = -5i + 5<br />
3j<br />
Perform the indicated operation.<br />
8) u = 9i + j, v = -4i - 2j, w = i - 8j; Find v - (u - w).<br />
Answer: -12i - 11j<br />
Find the magnitude and direction angle (to the nearest tenth) for the vector. Give the measure of the direction angle as an<br />
angle in [0,360°].<br />
9) -4, -3<br />
Answer: 5; 216.9°<br />
1
Find the angle between the given vectors to the nearest tenth of a degree.<br />
10) , <br />
Answer: 11.3°<br />
11) , <br />
Answer: 171.0°<br />
Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as<br />
an angle in [0,360°].<br />
12) 6, 6<br />
Answer: 6 2; 45°<br />
13) -5, 12<br />
Answer: 13; 112.6°<br />
Find the angle between the given vectors to the nearest tenth of a degree.<br />
14) , <br />
Answer: 84.6°<br />
15) , <br />
Answer: 32.9°<br />
Perform the indicated operation. Use the form for vectors.<br />
16) u = and v = ; Find u · v.<br />
Answer: -8<br />
2
Answer Key<br />
Testname: PRE CALCULUS<br />
ON 3-4-2011<br />
EXAM REVIEW VECTORS_WITH ANSWERS<br />
1) u = 5, v = 5; yes<br />
2) 15<br />
3) 2<br />
4) v = -3i - 9j<br />
5) 6i + 8j<br />
6) u = - 3 5 i - 4 5 j<br />
7) v = -5i + 5 3j<br />
8) -12i - 11j<br />
9) 5; 216.9°<br />
10) 11.3°<br />
11) 171.0°<br />
12) 6 2; 45°<br />
13) 13; 112.6°<br />
14) 84.6°<br />
15) 32.9°<br />
16) -8<br />
3
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