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

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:

The change in a vector may occur due to .....

$A$ vector $\vec{A}$ is rotated by a small angle $\Delta \theta$ radian $(\Delta \theta \ll 1)$ to get a new vector $\vec{B}$. In that case,$|\vec{B} - \vec{A}|$ is

$A$ force,$\vec{F}=(4 \hat{i}+3 \hat{j}-5 \hat{k}) \text{ N}$,is acting on a body. If the horizontal direction is taken along the $\hat{i} + \hat{j}$ direction,find the angle $\theta$ that the force makes with this horizontal direction.

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