Vector $\overrightarrow{A}$ makes equal angles with $x, y,$ and $z$ axes. The value of its components (in terms of the magnitude of $\overrightarrow{A}$) will be:

Two forces $F_1 = 1\,N$ and $F_2 = 2\,N$ act along the lines $x = 0$ and $y = 0$ respectively. Then the resultant of forces would be

Given: $\vec{A} = 2\hat{i} + p\hat{j} + q\hat{k}$ and $\vec{B} = 5\hat{i} + 7\hat{j} + 3\hat{k}$. If $\vec{A} \parallel \vec{B}$,then the values of $p$ and $q$ are,respectively:

The angles which a vector $\hat{i} + \hat{j} + \sqrt{2} \hat{k}$ makes with $X, Y$ and $Z$ axes respectively are

The vectors $(A + B)$ and $(A - B)$ are at right angles to each other. This is possible under the condition

Two vectors $\overrightarrow{X}$ and $\overrightarrow{Y}$ have equal magnitude. The magnitude of $(\overrightarrow{X}-\overrightarrow{Y})$ is $n$ times the magnitude of $(\overrightarrow{X}+\overrightarrow{Y})$. The angle between $\overrightarrow{X}$ and $\overrightarrow{Y}$ is: