How can we represent a vector quantity?

$A$ vector $\overrightarrow{a}$ is turned without a change in its length through a small angle $d\theta$. The values of $|\Delta \overrightarrow{a}|$ and $\Delta a$ are respectively:

$A$ unit vector is given by $a\hat{i} + b\hat{j} + c\hat{k}$. If the values of $a$ and $b$ are $0.6$ and $0.8$ respectively, find the value of $c$.

The position vectors of points $A, B, C$ and $D$ are $A = 3\hat{i} + 4\hat{j} + 5\hat{k}$,$B = 4\hat{i} + 5\hat{j} + 6\hat{k}$,$C = 7\hat{i} + 9\hat{j} + 3\hat{k}$ and $D = 4\hat{i} + 6\hat{j}$. Then the displacement vectors $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are:

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

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