Given : $\vec A\, = \,2\hat i\, + \,p\hat j\, + q\hat k$ and $\vec B\, = \,5\hat i\, + \,7\hat j\, + 3\hat k,$ if $\vec A\,||\,\vec B,$ then the values of $p$ and $q$ are, respectively

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

Given that $\vec A\, + \,\vec B\, = \,\vec C\,.$  If  $\left| {\vec A} \right|\, = \,4,\,\,\left| {\vec B} \right|\, = \,5\,\,$ and $\left| {\vec C} \right|\, =\,\sqrt {61}$ the angle between $\vec A\,\,$ and $\vec B$ is ....... $^o$

In the cube of side $a$ shown in the figure, the vector from the central point of the face $ABOD$ to the central point of the face $BEFO$ will be

Two forces having magnitude $A$ and $\frac{ A }{2}$ are perpendicular to each other. The magnitude of their resultant is

Given that $\overrightarrow A + \overrightarrow B + \overrightarrow C= 0$ out of three vectors two are equal in magnitude and the magnitude of third vector is $\sqrt 2 $ times that of either of the two having equal magnitude. Then the angles between vectors are given by