$ABC$ is an equilateral triangle. The length of each side is $a$ and the centroid is point $O$. Find $\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CA} = \ldots \ldots$.

Which of the following colours of visible light has the lowest energy?

Two vectors $\overrightarrow{X}$ and $\overrightarrow{Y}$ have equal magnitude. The magnitude of $(\overrightarrow{X}-\overrightarrow{Y})$ is $n$ times the magnitude of $(\overrightarrow{X}+\overrightarrow{Y})$. The angle between $\overrightarrow{X}$ and $\overrightarrow{Y}$ is:

If the vector $\vec{P} = 3\hat{i} + 4\hat{j} + 12\hat{k}$,then the magnitude of the vector $\vec{P}$ is ......

A body cools according to Newton's law of cooling from $100^\circ C$ to $60^\circ C$ in $20$ minutes. The temperature of the surroundings being $20^\circ C$, then the total time required for the body to cool down to $30^\circ C$ is

What is the position vector of a particle located at $(3, 2, 5)$?