If A = 2i + 2k and B = i + j, the angle between vector A and vector B is
A) 30°.
B) 45°.
C) 60°.
D) 90°.

Question

Quizplus · Accepted Answer

The angle θ between two vectors A and B can be found using the dot product formula: A · B = |A||B|cos(θ), where |A| and |B| are the magnitudes of vectors A and B, respectively. For vectors A = 2i + 2k and B = i + j, the dot product A · B = (2)(1) + (0)(1) + (2)(0) = 2. The magnitudes are |A| = sqrt((2)^2 + (0)^2 + (2)^2) = sqrt(8) and |B| = sqrt((1)^2 + (1)^2 + (0)^2) = sqrt(2). Thus, cos(θ) = 2 / (sqrt(8) * sqrt(2)) = 2 / 4 = 1/2, which corresponds to θ = 60°.

If a = 2i + 2k and B = I