The dot product of two mutually perpendicular vectors is:

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:

If a vector $2\hat i + 3\hat j + 8\hat k$ is perpendicular to the vector $4\hat j - 4\hat i + \alpha \hat k$,then the value of $\alpha$ is:

For any two vectors $\vec{A}$ and $\vec{B}$,if $\vec{A} \cdot \vec{B} = |\vec{A} \times \vec{B}|$,the magnitude of $(\vec{A} + \vec{B})$ is: $(\tan \frac{\pi}{4} = 1, \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}})$

Vector $\vec{A}$ of magnitude $5 \sqrt{3}$ units,another vector $\vec{B}$ of magnitude $10$ units are inclined to each other at an angle of $30^{\circ}$. The magnitude of the vector product of the two vectors is $\left[\sin 30^{\circ}=\frac{1}{2}\right]$

Write the necessary condition for the scalar product of two mutually perpendicular vectors.