Questions in vectors

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What is the angle between $\overrightarrow P $ and the resultant of $(\overrightarrow P + \overrightarrow Q )$ and $(\overrightarrow P - \overrightarrow Q )$
The resultant of $\overrightarrow P $ and $\overrightarrow Q $ is perpendicular to $\overrightarrow P $. What is the angle between $\overrightarrow P $ and $\overrightarrow Q $
Maximum and minimum magnitudes of the resultant of two vectors of magnitudes P and Q are in the ratio $3:1.$Which of the following relations is true
The resultant of two vectors $\overrightarrow P $ and $\overrightarrow Q $ is $\overrightarrow R .$ If Q is doubled, the new resultant is perpendicular to P. Then R equals
Two forces, ${F_1}$ and ${F_2}$ are acting on a body. One force is double that of the other force and the resultant is equal to the greater force. Then the angle between the two forces is
Given that $\overrightarrow A + \overrightarrow B = \overrightarrow C $and that $\overrightarrow C $ is $ \bot $ to $\overrightarrow A $. Further if $|\overrightarrow A |\, = \,|\overrightarrow C |,$then what is the angle between $\overrightarrow A $ and $\overrightarrow B $
A body is at rest under the action of three forces, two of which are ${\vec F_1} = 4\hat i,\,{\vec F_2} = 6\hat j,$the third force is
A plane is revolving around the earth with a speed of 100 km/hr at a constant height from the surface of earth. The change in the velocity as it travels half circle is
What displacement must be added to the displacement $25\hat i - 6\hat j\,\,m$ to give a displacement of 7.0 m pointing in the x- direction
A body moves due East with velocity 20 km/hour and then due North with velocity 15 km/hour. The resultant velocity

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