Find the Angle Between Two Vectors
-$\mathbf { u } = - \mathbf { i } + 2 \mathbf { j } , \mathbf { v } = 6 \mathbf { i } - 3 \mathbf { j }$
A) $143.1 ^ { \circ }$
B) $0.8 ^ { \circ }$
C) $90 ^ { \circ }$
D) $53.1 ^ { \circ }$

Question

Quizplus · Accepted Answer

The angle between two vectors $\mathbf{u}$ and $\mathbf{v}$ can be found using the dot product formula: $\mathbf{u} \cdot \mathbf{v} = |\mathbf{u}| |\mathbf{v}| \cos(\theta)$, where $\theta$ is the angle between the vectors. For $\mathbf{u} = -\mathbf{i} + 2\mathbf{j}$ and $\mathbf{v} = 6\mathbf{i} - 3\mathbf{j}$, the dot product is $(-1)(6) + (2)(-3) = -6 - 6 = -12$. The magnitudes are $|\mathbf{u}| = \sqrt{(-1)^2 + 2^2} = \sqrt{5}$ and $|\mathbf{v}| = \sqrt{6^2 + (-3)^2} = \sqrt{45}$. Substituting these into the formula gives $\cos(\theta) = \frac{-12}{\sqrt{5}\sqrt{45}}$, solving for $\theta$ yields $143.1^\circ$.

Find the Angle Between Two Vectors - u=−i+2j,v=6i−3j\mathbf { u } = - \mathbf { i } + 2 \mathbf { j } , \mathbf { v } = 6 \mathbf { i } - 3 \mathbf { j }u=−i+2j,v=6i−3j

Find the Angle Between Two Vectors
- $\mathbf { u } = - \mathbf { i } + 2 \mathbf { j } , \mathbf { v } = 6 \mathbf { i } - 3 \mathbf { j }$