Find the energy of the third stationary orbit of Bohr's model of the hydrogen atom if the energy of the ground state is $-E \text{ J}$.

For the resultant of two vectors $A$ and $B$ to be maximum,the angle between them should be (in $^{\circ}$)

$A$ force,$\vec{F}=(4 \hat{i}+3 \hat{j}-5 \hat{k}) \text{ N}$,is acting on a body. If the horizontal direction is taken along the $\hat{i} + \hat{j}$ direction,find the angle $\theta$ that the force makes with this horizontal direction.

The resultant of two vectors $A$ and $B$ makes an angle $\alpha$ with $A$ and $\beta$ with $B$. Which of the following is correct?

The vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane. Another vector $\overrightarrow{C}$ lies outside this plane. The resultant $\overrightarrow{R} = \overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C}$ of these three vectors:

The component of vector $\vec{A} = 2\hat{i} + 3\hat{j}$ along the vector $\vec{B} = \hat{i} + \hat{j}$ is: