The two vectors have magnitudes $3$ and $5$. If the angle between them is $60^o$,then the dot product of the two vectors will be:

$A$ vector $\overrightarrow{F}_1$ is along the positive $X$-axis. If its vector product with another vector $\overrightarrow{F}_2$ is zero,then $\overrightarrow{F}_2$ could be:

Find the component of vector $\vec{r}$ in the direction of vector $\vec{a}$.

Show that the magnitude of a vector is equal to the square root of the scalar product of the vector with itself.

If $\vec{a}$ and $\vec{b}$ make an angle $\cos^{-1}\left(\frac{5}{9}\right)$ with each other,then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$. The integer value of $n$ is . . . . . . .

If a vector $\vec A$ is parallel to another vector $\vec B$,then the resultant of the vector $\vec A \times \vec B$ will be equal to