There are four forces acting at a point $P$ produced by strings as shown in figure, point $P$ is at rest. The forces $F_1$ and $F_2$ are respectively:-
$\frac{1}{\sqrt 2}N,\frac{3}{\sqrt 2}N$
$\frac{3}{\sqrt 2}N,\frac{1}{\sqrt 2}N$
$\frac{1}{\sqrt 2}N,\frac{1}{\sqrt 2}N$
$\frac{3}{\sqrt 2}N,\frac{3}{\sqrt 2}N$
Four forces are acting at a point $P$ in equilibrium as shown in figure. The ratio of force $F_{1}$ to $F_{2}$ is $1: x$ where $x =....$
The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\overrightarrow{\mathrm{A}}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is . . . . . .
The angles which a vector $\hat i + \hat j + \sqrt 2 \,\hat k$ makes with $X, Y$ and $Z$ axes respectively are
Following forces start acting on a particle at rest at the origin of the co-ordinate system simultaneously${\overrightarrow F _1} = - 4\hat i - 5\hat j + 5\hat k$, ${\overrightarrow F _2} = 5\hat i + 8\hat j + 6\hat k$, ${\overrightarrow F _3} = - 3\hat i + 4\hat j - 7\hat k$ and ${\overrightarrow F _4} = 2\hat i - 3\hat j - 2\hat k$ then the particle will move
A motorboat is racing towards north at $25\; km / h$ and the water current in that region is $10\; km / h$ in the direction of $60^{\circ}$ east of south. Find the resultant velocity of the boat.