Find the Angle Between Two Vectors
-$\mathbf { u } = \mathbf { i } - \mathbf { j } , \mathbf { v } = 4 \mathbf { i } + 5 \mathbf { j }$
A) $96.3 ^ { \circ }$
B) $6.3 ^ { \circ }$
C) $99 ^ { \circ }$
D) $- 6.3 ^ { \circ }$

Question

Quizplus · Accepted Answer

The angle between two vectors $\mathbf{u}$ and $\mathbf{v}$ can be found using the dot product formula: $\cos \theta = \frac{\mathbf{u} \cdot \mathbf{v}}{\|\mathbf{u}\| \|\mathbf{v}\|}$. For $\mathbf{u} = \mathbf{i} - \mathbf{j}$ and $\mathbf{v} = 4\mathbf{i} + 5\mathbf{j}$, $\mathbf{u} \cdot \mathbf{v} = (1)(4) + (-1)(5) = -1$, $\|\mathbf{u}\| = \sqrt{1^2 + (-1)^2} = \sqrt{2}$, and $\|\mathbf{v}\| = \sqrt{4^2 + 5^2} = \sqrt{41}$. Thus, $\cos \theta = \frac{-1}{\sqrt{2} \sqrt{41}}$, leading to $\theta \approx 96.3^\circ$.

Find the Angle Between Two Vectors - u=i−j,v=4i+5j\mathbf { u } = \mathbf { i } - \mathbf { j } , \mathbf { v } = 4 \mathbf { i } + 5 \mathbf { j }u=i−j,v=4i+5j

Find the Angle Between Two Vectors
- $\mathbf { u } = \mathbf { i } - \mathbf { j } , \mathbf { v } = 4 \mathbf { i } + 5 \mathbf { j }$