If a unit vector is represented by $\vec{U} = 0.9\hat{i} - 0.2\hat{j} + m\hat{k}$, then the value of $m$ is

The unit vector $(a \hat{\imath} + b \hat{\jmath})$ is perpendicular to $(\hat{\imath} + \hat{\jmath})$. The value of $b$ is

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

$A$ 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 = $

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

$\overrightarrow{A} = 4\hat{i} + 3\hat{j}$ and $\overrightarrow{B} = 4\hat{i} + 2\hat{j}$. Find a vector parallel to $\overrightarrow{A}$ but with a magnitude five times that of $\overrightarrow{B}$.