Find the angle between the vectors u and v if $\mathbf { u } = \langle 3 , - 3 \rangle$ , and $\mathbf { v } = \langle 1 , - 1 \rangle$ Round your answer to two decimal places.
A)1.41°
B)0.00°
C)-1.24°
D)-1.93°
E)0.96°

Question

Quizplus · Accepted Answer

The angle between two vectors $\mathbf{u}$ and $\mathbf{v}$ can be found using the dot product formula: $\cos(\theta) = \frac{\mathbf{u} \cdot \mathbf{v}}{\|\mathbf{u}\|\|\mathbf{v}\|}$. Here, $\mathbf{u} \cdot \mathbf{v} = (3)(1) + (-3)(-1) = 3 + 3 = 6$, $\|\mathbf{u}\| = \sqrt{3^2 + (-3)^2} = \sqrt{18}$, and $\|\mathbf{v}\| = \sqrt{1^2 + (-1)^2} = \sqrt{2}$. Plugging these into the formula gives $\cos(\theta) = \frac{6}{\sqrt{18}\sqrt{2}} = 1$, which means $\theta = \cos^{-1}(1) = 0^\circ$. Therefore, the vectors are parallel, and the angle between them is 0.00°.

Find the Angle Between the Vectors U and V If u=⟨3,−3⟩\mathbf { u } = \langle 3 , - 3 \rangleu=⟨3,−3⟩

Find the Angle Between the Vectors U and V If $\mathbf { u } = \langle 3 , - 3 \rangle$