Questions in statics

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The resultant of two forces P and Q is at right angles to P, the resultant of P and ${Q}'$ acting at the same angle $\alpha $is at right angles to ${Q}'$. Then,
The resultant R of two forces P and Q act at right angles to P. Then the angle between the forces is
The sum of the two forces is 18 and their resultant perpendicular to the lesser of the forces is 12, then the lesser force is
The magnitudes of two forces are 3, 5 and the direction of the resultant is at right angles to that of the smaller force. The ratio of the magnitude of the larger force and of the resultant is
If the resultant of two forces $P$ and $Q$ is $\sqrt{3}Q$ and makes an angle $30^o$ with the direction of $P$, then
The resolved part of a force of 16 Newton in a direction is $8\sqrt{3}$ Newton. The inclination of the direction of the resolved part with the direction of the force is
Let P, 2P and 3P be the forces acting along AB, BC, CA of an equilateral $\Delta ABC$. Suppose R is the magnitude of their resultant and $\theta $the angle made by the resultant with the side BC, then
When a particle be kept at rest under the action of the following forces
In a triangle ABC three forces of magnitudes $3\overrightarrow{AB},\ 2\overrightarrow{AC}$and $6\overrightarrow{CB}$are acting along the sides AB, AC and CB respectively. If the resultant meets AC at $D$, then the ratio DC : AD will be equal to
If the forces of 12, 5 and 13 unit-wt balance at a point, two of them are inclined at

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