$A$ force ${F_1} = 1\,N$ acts along the direction of $x = 0$,and a force ${F_2} = 2\,N$ acts along the direction of $y = 0$. Find the resultant force.

The resultant of two forces $3P$ and $2P$ is $R$. If the first force is doubled,then the resultant is also doubled. The angle between the two forces is ........... $^o$.

The unit vector parallel to the resultant of the vectors $\vec A = 4\hat i + 3\hat j + 6\hat k$ and $\vec B = - \hat i + 3\hat j - 8\hat k$ is

$A$ vector $\vec Q$ which has a magnitude of $8$ is added to the vector $\vec P$ which lies along the $x$-axis. The resultant of the two vectors lies along the $y$-axis and has a magnitude twice that of $\vec P$. The magnitude of $\vec P$ is:

If $\overrightarrow{A} = 3\widehat{i} + 2\widehat{j}$ and $\overrightarrow{B} = \widehat{i} + \widehat{j} - 2\widehat{k}$,find their sum using the algebraic method.

Forces $F_1$ and $F_2$ act on a point mass in two mutually perpendicular directions. The resultant force on the point mass will be