Find the angle between u and v in radians.
-u = 7j - 2k, v = 4i - 6j - 7k
A) -0.39
B) 1.75
C) 1.96
D) 1.58

Question

Quizplus · Accepted Answer

The angle θ between two vectors u and v can be found using the dot product formula: u · v = |u||v|cos(θ). First, calculate the dot product u · v = (0)(4) + (7)(-6) + (-2)(-7) = -42 + 14 = -28. Then, find the magnitudes: |u| = √(0^2 + 7^2 + (-2)^2) = √53 and |v| = √(4^2 + (-6)^2 + (-7)^2) = √101. Now, cos(θ) = -28 / (√53 * √101). Solving for θ gives θ ≈ 1.96 radians.

Find the Angle Between U and V in Radians