0 like 0 dislike
97 views
Knowing the dot product of two vectors, how can I establish the angle between them?
| 97 views

0 like 0 dislike

Rewriting the formula

$$\mathbf{u} \cdot \mathbf{v}=\|\mathbf{u}\|\|\mathbf{v}\| \cos \theta$$

we can rearrange and obtain

$$\cos \theta=\frac{\mathbf{u} \cdot \mathbf{v}}{\|\mathbf{u}\|\|\mathbf{v}\|}$$

Since $0 \leq \theta \leq \pi$, it follows and properties of the cosine function studied in trigonometry that

• $-\theta$ is acute if $\mathbf{u} \cdot \mathbf{v}>0$
• $\theta$ is obtuse if $\mathbf{u} \cdot \mathbf{v}<0$
• $\theta=\pi / 2$ if $\mathbf{u} \cdot \mathbf{v}=0$.
by Platinum (130,532 points)
selected by

0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
1 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike