What is the angle between the two vectors a = (1, 0) and b = (1, 1) in the Cartesian plane?
Answer and explanation
Correct answer: A. 45° (pi/4 rad)
The angle theta between vectors satisfies cos(theta) = (a · b) / (|a| |b|). Here a · b = (11 + 01) = 1. The magnitudes are |a| = sqrt(1^2 + 0^2) = 1, and |b| = sqrt(1^2 + 1^2) = sqrt(2). Thus, cos(theta) = 1 / (1 sqrt(2)) = 1 / sqrt(2) = sqrt(2) / 2. Therefore, theta = 45° (or pi/4 radians).
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