The sum of magnitude of two forces acting at a point is $16N$ and their resultant $8\sqrt 3 \,\,N$ is at ${90^0}$ with the force of smaller magnitude. The two forces $\left( {in\,\,N} \right)$ are

Two forces $\vec{F_1}$ and $\vec{F_2}$ act on a particle. $\vec{F_1}$ has a magnitude of 10 N and acts along the positive x-axis. $\vec{F_2}$ has a magnitude of 5 N and acts at an angle of 120° with respect to the positive x-axis. If the resultant force $\vec{R}$ makes an angle $heta$ with $\vec{F_1}$, then $an(heta)$ is:

Two forces of equal magnitude F act on an object. For which angle between the forces will the magnitude of the resultant be maximum?

Two vectors A and B have magnitudes 4 and 5 units respectively. If the magnitude of their resultant is $\sqrt{61}$, what is the angle between the two vectors?

If the sum of the two unit vectors is also a unit vector, then magnitude of their difference is

The resultant of two forces 3P and 2P is R. If the first force is doubled them the resultant is also doubled. The angle between the two forces is

There are two forces each of magnitude 10 units. One inclined at an angle of ${30^0}$ and the other at an angle of ${135^0}$ to the positive direction of x-axis. The x and y components of the resultant are respectively.

A boat is rowed across a river with a velocity $v$ perpendicular to the flow of the river. The river flows with a velocity $u$. The magnitude of the resultant velocity of the boat is:

If three vectors acting simultaneously on a particle can be represented in magnitude and direction by the three sides of a triangle taken in order, then the particle will:

The resultant of two forces, one doubled the other in magnitude is perpendicular to the smaller of the forces. The angle between the two forces is

Two vectors $\vec{A}$ and $\vec{B}$ are added using the parallelogram law. If the magnitude of $\vec{A}$ is doubled while keeping the magnitude of $\vec{B}$ and the angle between them constant, how does the magnitude of the resultant vector change?