Find the angle θ between the vectors. $\begin{array} { l }
\mathbf { u } = \langle 6,2 \rangle \
\mathbf { v } = \langle 7,0 \rangle
\end{array}$ (Round the answer to 2 decimal places. )

A) $18.43 ^ { \circ }$
B) $33.43 ^ { \circ }$
C) $23.43 ^ { \circ }$
D) $28.43 ^ { \circ }$
E) $38.43 ^ { \circ }$

Question

Find the angle θ between the vectors.​ $\begin{array} { l } 
\mathbf { u } = \langle 6,2 \rangle \
\mathbf { v } = \langle 7,0 \rangle
\end{array}$ ​ (Round the answer to 2 decimal places. )
​
A) $18.43 ^ { \circ }$
B) $33.43 ^ { \circ }$
C) $23.43 ^ { \circ }$
D) $28.43 ^ { \circ }$
E) $38.43 ^ { \circ }$

Quizplus · Accepted Answer

The angle θ can be found using the dot product formula: $ \mathbf{u} \cdot \mathbf{v} = \|\mathbf{u}\| \|\mathbf{v}\| \cos \theta $. The dot product is $6 \times 7 + 2 \times 0 = 42$. The magnitudes are $\|\mathbf{u}\| = \sqrt{6^2 + 2^2} = \sqrt{40}$ and $\|\mathbf{v}\| = \sqrt{7^2} = 7$. Thus, $\cos \theta = \frac{42}{\sqrt{40} \times 7}$. Solving for θ gives approximately $18.43^\circ$.

Find the Angle θ Between the Vectors u=⟨6,2⟩v=⟨7,0⟩\begin{array} { l } \mathbf { u } = \langle 6,2 \rangle \\\mathbf { v } = \langle 7,0 \rangle\end{array}u=⟨6,2⟩v=⟨7,0⟩​

Find the Angle θ Between the Vectors $\begin{array} { l } \mathbf { u } = \langle 6,2 \rangle \\\mathbf { v } = \langle 7,0 \rangle\end{array}$