If $\vec{a}$ and $\vec{b}$ are two unit vectors such that $|\vec{a} + \vec{b}| = \sqrt{3}$, then the value of $(3\vec{a} - 4\vec{b}) \cdot (2\vec{a} + 5\vec{b})$ is:

Vector $\vec A$ has magnitude of 5 unit directed along east, then vector $6\vec A$

If the dot product of two non-zero vectors is zero, what can be concluded about the angle between them?

Two vectors \vec{a} and \vec{b} satisfy the condition |\vec{a} + \vec{b}|^2 = |\vec{a}|^2 + |\vec{b}|^2. What is the angle between \vec{a} and \vec{b}?

The sum of two vectors ${\rm{\vec A}}\,and\,{\rm{\vec B}}$ is at right angles to their difference. Then

Find the angle between two vectors $\overrightarrow A = 2\widehat i + \widehat j - \widehat k$ and $\overrightarrow B = \widehat i - \widehat k$

Velocity and acceleration vectors of a charged particle moving perpendicular to the direction of magnetic field at a given instant of time are $\overrightarrow V = 2\widehat i + c\widehat j\,and\,\overrightarrow a = 3\widehat i + 4\widehat j$ respectively. Then the value of ‘C’ is

The dot product of two vectors A and B is zero. What is the angle between them?

A force F acts on a block, causing it to move a distance d. If the angle between F and d is obtuse, what can be said about the work done by the force?

Two displacements, $\vec{d_1}$ and $\vec{d_2}$, have magnitudes $d_1$ and $d_2$ respectively. If $|d_1 + d_2| = |d_1 - d_2|$, find the dot product $\vec{d_1} \cdot \vec{d_2}$.

The angle between the two vectors $\overrightarrow A = \widehat i + 2\widehat j - \widehat k\,and\,\overrightarrow B = - \widehat i + \widehat j - 2\widehat k$ is