Find the angle between v and w. Round to one decimal place, if necessary.
-v = 2i + j - 2k and w = i + 3j - 3k
A) 32.7°
B) 55.6°
C) 57.3°
D) 67.3°

Question

Quizplus · Accepted Answer

The angle θ between two vectors v and w can be found using the dot product formula: cos(θ) = (v · w) / (||v|| ||w||), where v · w is the dot product of v and w, and ||v|| and ||w|| are the magnitudes of v and w, respectively. For v = 2i + j - 2k and w = i + 3j - 3k, v · w = (2)(1) + (1)(3) + (-2)(-3) = 2 + 3 + 6 = 11. The magnitudes are ||v|| = sqrt((2)^2 + (1)^2 + (-2)^2) = sqrt(4 + 1 + 4) = sqrt(9) = 3, and ||w|| = sqrt((1)^2 + (3)^2 + (-3)^2) = sqrt(1 + 9 + 9) = sqrt(19). Thus, cos(θ) = 11 / (3sqrt(19)), and θ ≈ 32.7°.

Find the Angle Between V and W