Two vectors $\vec{A}$ and $\vec{B}$ have magnitudes A and B respectively. If the magnitude of their resultant is $\sqrt{A^2 + B^2 + \sqrt{3}AB}$, the angle between the vectors is:

A child travelling in a train throws a ball outside with a speed V. According to a child who is standing on the ground, the speed of the ball is

A boat attempts to cross a river flowing with a velocity of $5\, m/s$. The boat can move with a speed of $10 \, m/s$ in still water. At what angle with respect to the upstream direction should the boat be steered to cross the river in the shortest possible distance?

\mathop {{\rm{ }}A}\limits^ -   = \mathop {{\rm{ }}B}\limits^ -   + \mathop {{\rm{ }}C}\limits^ -   and the magnitudes of \mathop {{\rm{ }}A}\limits^ -  ,\mathop {{\rm{ }}B}\limits^ -  ,\mathop {{\rm{ }}C}\limits^ -   are 5, 4 and 3 units respectively, the angle between \mathop {{\rm{ }}A}\limits^ -  \mathop {{\rm{ }}C}\limits^ -   is:

If the vector ${\rm{\vec A}} = 2\hat i + 4\hat j\,\,and\,\,{\rm{\vec B}} = 5\hat i + {\rm{p\hat j}}$ are parallel to each other, the magnitude of ${\rm{\vec B}}$ is

\mathop {{\rm{ }}A}\limits^ -   = \mathop {{\rm{ }}B}\limits^ -   + \mathop {{\rm{ }}C}\limits^ -   and the magnitudes of \mathop {{\rm{ }}A}\limits^ -  ,\mathop {{\rm{ }}B}\limits^ -  ,\mathop {{\rm{ }}C}\limits^ -   are 5, 4 and 3 units respectively, the angle between \mathop {{\rm{ }}A}\limits^ -  \mathop {{\rm{ }}C}\limits^ -   is:

If a vector $\vec{A}$ is resolved into two perpendicular components $A_x$ and $A_y$, and the magnitude of $A_x$ is twice the magnitude of $A_y$, what is the angle between $\vec{A}$ and the x-axis?

A river flows due east with a speed of 3 m/s. A man can swim in still water at a speed of 5 m/s. If he wants to cross the river in the shortest possible time, the angle at which he should swim with respect to the north is:

A vector has a magnitude of 5 units and is directed along the positive x-axis. What are its components?

What vector must be added to the sum of two vectors $2\hat i - \hat j + 3\hat k\,and\,3\hat i - 2\hat j - 2\hat k$ so that the resultant is a unit vector along Z-axis.

Two vectors of equal magnitude are acting at a point. If the magnitude of their resultant is equal to the magnitude of either of the vectors, what is the angle between the two vectors?