20
QuizMultiple Choice

Modeling with Vector Quantities — Test

Question 20 • Precalculus

Let magnitude of vector r is equal to 6 at an angle of 30 degrees and magnitude of vector s is equal to 11 at an angle of 225 degrees Which expression represents magnitude of vector r minus vector s ?

Answer
A
square root of 6 squared plus 11 squared minus 2 6 11 cosine open paren 165 degrees close paren end root
B
square root of 6 squared plus 11 squared minus 2 6 11 cosine open paren 45 degrees close paren end root
C
square root of 6 squared plus 11 squared minus 2 6 11 cosine open paren 255 degrees close paren end root
D
square root of 6 squared plus 11 squared minus 2 6 11 cosine open paren 15 degrees close paren end root

Explanation

Use the formula |r − s| = √(|r|² + |s|² − 2|r||s|cos θ), where θ is the angle between the vectors. Their direction angles differ by 225° − 30° = 195°, and cos(195°) = cos(165°). Therefore the expression uses cos(165°), matching choice A.

AI-written and checked against the verified answer.

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