Find the angle between the vectors u = (1, 1) and v = (1, 0).
Answer and explanation
Correct answer: B. pi/4 (45 degrees)
- Step 1: Use the formula cos(theta) = (u . v) / (||u|| * ||v||).
- Step 2: u . v = (1)(1) + (1)(0) = 1. ||u|| = sqrt(1^2 + 1^2) = sqrt(2), and ||v|| = 1. cos(theta) = 1 / sqrt(2) = sqrt(2)/2, which gives theta = pi/4.
Answer
pi/4 (45 degrees).
Why not the others: 'pi/3 (60 degrees)' corresponds to cos(theta) = 1/2; 'pi/6 (30 degrees)' corresponds to cos(theta) = sqrt(3)/2; 'pi/2 (90 degrees)' corresponds to orthogonal vectors.
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