$A$ vector $\vec{P}$ makes angles $\alpha, \beta,$ and $\gamma$ with the $X, Y,$ and $Z$ axes respectively. Then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = $

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

Assertion $A$: If $A, B, C, D$ are four points on a semi-circular arc with centre at $O$ such that $|\overrightarrow{AB}|=|\overrightarrow{BC}|=|\overrightarrow{CD}|$,then $\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}=4\overrightarrow{AO}+\overrightarrow{OB}+\overrightarrow{OC}$.
Reason $R$: Polygon law of vector addition yields $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}+\overrightarrow{AD}=2\overrightarrow{AO}$.
In the light of the above statements,choose the most appropriate answer from the options given below.

Give three properties which have different magnitudes and also have different directions.

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

Find the magnitude and direction of the vector $\vec{A} = \hat{i} + \hat{j}$.