Find the angle between the vectors for u and v. $$\mathbf { u } = 6 \mathbf { i } + 4 \mathbf { j } , \mathbf { v } = 5 \mathbf { i } + 3 \mathbf { j }$$
A) $48.22 ^ { \circ }$
B) $2.73 ^ { \circ }$
C) $87.27 ^ { \circ }$
D) $44.97 ^ { \circ }$
E) $88.64 ^ { \circ }$

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 $\mathbf{u} = 6\mathbf{i} + 4\mathbf{j}$ and $\mathbf{v} = 5\mathbf{i} + 3\mathbf{j}$, the dot product $\mathbf{u} \cdot \mathbf{v} = 6*5 + 4*3 = 30 + 12 = 42$. The magnitudes are $\|\mathbf{u}\| = \sqrt{6^2 + 4^2} = \sqrt{36 + 16} = \sqrt{52}$ and $\|\mathbf{v}\| = \sqrt{5^2 + 3^2} = \sqrt{25 + 9} = \sqrt{34}$. Thus, $\cos(\theta) = \frac{42}{\sqrt{52}\sqrt{34}}$, and solving for $\theta$ gives an angle close to $2.73^\circ$.

Find the Angle Between the Vectors for U and V u=6i+4j,v=5i+3j\mathbf { u } = 6 \mathbf { i } + 4 \mathbf { j } , \mathbf { v } = 5 \mathbf { i } + 3 \mathbf { j }u=6i+4j,v=5i+3j

Find the Angle Between the Vectors for U and V $\mathbf { u } = 6 \mathbf { i } + 4 \mathbf { j } , \mathbf { v } = 5 \mathbf { i } + 3 \mathbf { j }$