The resultant of two vectors at an angle $150^{\circ}$ is $10$ units and is perpendicular to one vector. The magnitude of the smaller vector is ....... units

The magnitude of a given vector with end points $ (4, -4, 0)$ and $(-2, -2, 0)$ must be

Two forces $3\,N$ and $2\, N$ are at an angle $\theta$ such that the resultant is $R$. The first force is now increased to $ 6\,N$ and the resultant become $2R$. The value of is ....... $^o$

Two forces each numerically equal to $10$ $dynes$ are acting as shown in the adjoining figure, then the magnitude of resultant is.........$dyne$

The two vectors $\vec A = -2\widehat i + \widehat j + 3\widehat k$ and $\vec B = 7\widehat i + 5\widehat j + 3\widehat k$ are :-

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 $