If a unit vector is represented by $0.5\hat i + 0.8\hat j + c\hat k$,then the value of $c$ is

Which of the following elements is doped to a fiber amplifier in an optical fiber communication system?

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:

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

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

Three forces of $3 \ N$,$4 \ N$,and $12 \ N$ act at a point in mutually perpendicular directions. Find the magnitude of the resultant force in $N$.