Two forces represented by vectors 3i + 4j and 5i - 2j act on a particle. What is the magnitude of the resultant force?

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

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 $\vec{B}$ have magnitudes A and B respectively. If the magnitude of their resultant vector is $\sqrt{A^2 + B^2 + \sqrt{3}AB}$, which of the following is the most accurate measure of the angle between $\vec{A}$ and $\vec{B}$?

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

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

Two forces of 6 N and 8 N act at a point at right angles to each other. What is the magnitude of their resultant force?

If $\overrightarrow A = 4\widehat i - 3\widehat j\,\,and\,\overrightarrow B = 6\widehat i - 8\widehat j$ then the magnitude and direction of $\overrightarrow A \, + \,\overrightarrow B$ will be

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.

Two forces of magnitudes $F_1$ and $F_2$ act on a particle. The resultant force has a magnitude $F_R$. If the angle between $F_1$ and $F_2$ is increased, keeping their magnitudes constant, which of the following is true about the magnitude of the resultant force $F_R$?

Three forces $\vec{F_1} = 2\hat{i} + \hat{j}$, $\vec{F_2} = \hat{i} - \hat{j}$, and $\vec{F_3} = x\hat{i} + y\hat{j}$ act on a particle. If the particle is in equilibrium, what are the values of $x$ and $y$?