Find the angle (in degrees) between vectors A = 2i + j - k and B = i + j.

30 deg
45 deg
60 deg
90 deg

Correct answer: 30 deg

Solution

Dot product A.B = 2+1+0 = 3. |A| = sqrt(6), |B| = sqrt(2). cos(theta) = 3/sqrt(12) = 3/(2*sqrt(3)) = sqrt(3)/2. So theta = 30 deg. Wait: 3/sqrt(12) = 3/(2*sqrt(3)) = (3*sqrt(3))/(2*3) = sqrt(3)/2. cos(theta) = sqrt(3)/2 => theta = 30 deg.

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