If vector u has length 4 and vector v has length 5, and the angle between them is 60 degrees, find u . v.
Answer and explanation
Correct answer: A. 10
- Step 1: Use the definition of dot product: u . v = ||u|| ||v|| cos(theta).
- Step 2: u . v = 4 5 cos(60 degrees) = 20 * (1/2) = 10.
Answer
10.
Why not the others: '20' assumes cos(0) = 1; '10*sqrt(3)' uses sin(60 degrees) = sqrt(3)/2 instead of cos(60 degrees); '15' uses (3/4) multiplier.
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