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

If $\overrightarrow{A}$ is a vector with magnitude $(3, 4)$,show that the magnitude of its unit vector is $1$.

The angle between the two vectors $\vec A = 3\hat i + 4\hat j + 5\hat k$ and $\vec B = 3\hat i + 4\hat j + 5\hat k$ is ....... $^o$

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.

Find the unit vector in the direction of $2\hat{i} + 3\hat{j} + 4\hat{k}$.

What is the result of multiplying a vector $\overrightarrow{A}$ by a positive real number $\lambda$?