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:

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:

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 forces of magnitudes $5\, N$ and $12\, N$ act on a particle at an angle of $90^\circ$ with each other. What is the magnitude of their resultant?

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

Given ${\rm{\vec A}} = \hat i + 2\hat j - 3\hat k$. When a vector ${\rm{\vec B}}$ is added to ${\rm{\vec A}}$, We get a unit vector along X=axis. Then,${\rm{\vec B}}$ is

The component of a vector $\vec{r}$ along the X-axis will have maximum value if:

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

A particle is projected with velocity $\vec{v} = (6\hat{i} + 8\hat{j})$ m/s. If $g = 10 m/s^2$, the radius of curvature of its trajectory at the highest point 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 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