Let |a| = 12 at an angle of 25° and |b| = 7 at an angle of 105°. What is the magnitude of a + b? Round to the nearest decimal.
Answer
A
12.8
B
14.9
C
15.4
D
17.3
Explanation
The angle between the vectors is 105° − 25° = 80°. Using the magnitude formula, |a + b| = √(12² + 7² + 2·12·7·cos 80°) ≈ √222.2 ≈ 14.9. So the magnitude is 14.9, choice B.
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