Question

good morning please tell

if v and u are two vectors and r is their resultant and r is perpendicular to v and 1/2 of u then what is angle between v and u

Answer 1

If $v$ and $u$ are two vectors and $r$ is their resultant and $r$ is perpendicular to $v$ and $1/2$ of $u$ then what is angle between $v$ and $u$

Solution:

The beginning of the vector $\vec{r}$ - the beginning of the vector $\vec{v}$ and the end vector $\vec{r}$ - end of the vector $\vec{u}$

$$\vec {u} + \vec {v} = \vec {r}$$ $$| \vec {r} | = \frac {1}{2} | \vec {u} |$$

We have a right triangle ABC, we can simply find the sine of the angle alpha ( $\alpha -$

the angle between the vectors $\vec{u}$ and $\vec{v}$ )

$$\sin \alpha = \frac {A C}{A B} = \frac {| \vec {r} |}{| \vec {u} |} = \frac {\frac {1}{2} | \vec {u} |}{| \vec {u} |} = \frac {1}{2}$$ $$\alpha = 3 0 ^ {0} \left(\frac {\pi}{6}\right)$$

Answer: angle between $\vec{u}$ and $\vec{v}$ is $\alpha = 30{}^{\circ}\left(\frac{\pi}{6}\right)$