Find the angle between u and v in radians.
-u = 8i, v = 7i - 9j
A) 0.91
B) 0.66
C) 1.28
D) 1.56

Question

Quizplus · Accepted Answer

The angle between two vectors $ \mathbf{u} $ and $ \mathbf{v} $ can be found using the dot product formula: $$ \cos(\theta) = \frac{\mathbf{u} \cdot \mathbf{v}}{\|\mathbf{u}\|\|\mathbf{v}\|} $$ Given $ \mathbf{u} = 8i $ and $ \mathbf{v} = 7i - 9j $, the dot product $ \mathbf{u} \cdot \mathbf{v} = 8*7 + 0*-9 = 56 $. The magnitudes are $ \|\mathbf{u}\| = 8 $ and $ \|\mathbf{v}\| = \sqrt{7^2 + (-9)^2} = \sqrt{49 + 81} = \sqrt{130} $. Thus, $$ \cos(\theta) = \frac{56}{8\sqrt{130}} = \frac{7}{\sqrt{130}} $$ Solving for $ \theta $, we find $ \theta \approx 0.91 $ radians.

Find the Angle Between U and V in Radians