Let $\theta$ be the angle between vectors $\vec{A}$ and $\vec{B}$. Which of the following figures correctly represents the angle $\theta$?

Calculate the de Broglie wavelength of an electron in the first Bohr orbit of a hydrogen atom if the velocity of an electron in the first orbit is $2.2 \times 10^6 \text{ m s}^{-1}$. [mass of electron = $9.1 \times 10^{-31} \text{ kg}$, Planck's constant $(h)$ = $6.626 \times 10^{-34} \text{ J s}$]

Which of the following is a unit vector?

If $\vec{P} \cdot \vec{Q} = 0$ and $\vec{P} \times \vec{Q} = PQ$,then what is the angle between $\vec{P}$ and $\vec{Q}$ (in $^{\circ}$)?

If a unit vector is represented as $\overrightarrow{u} = 0.4 \hat{i} + 0.7 \hat{j} + c \hat{k}$,then the value of '$c$' is

If a vector $\overrightarrow{P}$ makes angles $\alpha, \beta,$ and $\gamma$ with the $X, Y,$ and $Z$ axes respectively,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = $