Find the angle between v and w. Round to one decimal place, if necessary.
-v = i + j and w = i + j - k
A) 66°
B) 0°
C) 35.3°
D) 90°

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||). For v = i + j and w = i + j - k, v · w = 1*1 + 1*1 + 0*(-1) = 2, ||v|| = sqrt(1^2 + 1^2) = sqrt(2), and ||w|| = sqrt(1^2 + 1^2 + (-1)^2) = sqrt(3). Thus, cos(θ) = 2 / (sqrt(2) * sqrt(3)) = sqrt(2/3), and θ ≈ 35.3°.

Find the Angle Between V and W