Three coplanar forces $\vec{F_1}$, $\vec{F_2}$, and $\vec{F_3}$ act on a point object such that the object is in equilibrium. If $|\vec{F_1}| = 10$ N, $|\vec{F_2}| = 15$ N and the angle between $\vec{F_1}$ and $\vec{F_2}$ is 60°, then the magnitude of $\vec{F_3}$ is closest to:

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.

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

Two forces are such that the sum of their magnitudes is 18N and their resultant is perpendicular to the smaller force and magnitude of the resultant is 12N . Then the magnitudes of the forces are

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

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

Two forces, each of magnitude $F$, act at a point at an angle $heta$. If the resultant force has the same magnitude $F$, the angle $heta$ is:

The adjacent sides of a parallelogram are $\overrightarrow A = 2\widehat i - 3\widehat j + \widehat k\,and\,\overrightarrow B = - 2\widehat i + 4\widehat j - \widehat k$ . Then the area of the parallelogram is

If the magnitude of the resultant of two vectors of equal magnitude is equal to the magnitude of either vector, what is the angle between the two vectors?

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: