Find the Angle Between Two Vectors
-$$\mathbf { u } = - 3 \mathbf { i } + 9 \mathbf { j } , \mathbf { v } = - 2 \mathrm { i } + 5 \mathbf { j }$$
A) $3.4 ^ { \circ }$
B) $13.4 ^ { \circ }$
C) $1.7 ^ { \circ }$
D) $351.7 ^ { \circ }$

Question

Quizplus · Accepted Answer

The dot product of the two vectors is:$$\mathbf { u } \cdot \mathbf { v } = (-3)(-2) + (9)(5) = 45$$The magnitude of the two vectors are:$$\left \| \mathbf { u } ight \| = \sqrt{(-3)^2 + (9)^2} = 3\sqrt{10}$$$$\left \| \mathbf { v } ight \| = \sqrt{(-2)^2 + (5)^2} = \sqrt{29}$$The angle between the two vectors is:$$	heta = \cos^{-1}\left(\frac{\mathbf { u } \cdot \mathbf { v } }{\left \| \mathbf { u } ight \| \left \| \mathbf { v } ight \|}ight) = \cos^{-1}\left(\frac{45}{3\sqrt{10} \sqrt{29}}ight) \approx 3.4^\circ$$

Find the Angle Between Two Vectors - u=−3i+9j,v=−2i+5j\mathbf { u } = - 3 \mathbf { i } + 9 \mathbf { j } , \mathbf { v } = - 2 \mathrm { i } + 5 \mathbf { j }u=−3i+9j,v=−2i+5j

Find the Angle Between Two Vectors
- $\mathbf { u } = - 3 \mathbf { i } + 9 \mathbf { j } , \mathbf { v } = - 2 \mathrm { i } + 5 \mathbf { j }$