A projectile is launched with an initial velocity $v_0$ at an angle $heta$ with the horizontal. At the highest point of its trajectory, the ratio of its potential energy to its kinetic energy 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.

\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:

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?

If a vector $2\hat{i}+3\hat{j}+8\hat{k}$ is perpendicular to the vector $4\hat{j}-4\hat{i}+\alpha\hat{k}$, then the value of $\alpha$ is:

Two forces of 5 N and 10 N act at a point. If the angle between them is 60°, what is the magnitude of their resultant?

Two vectors of magnitudes 5 and 10 units are inclined at an angle of 60° to each other. What is the magnitude of their resultant?

A vector $\vec{A}$ points vertically upward and $\vec{B}$ points towards north. The vector product $\vec{A} imes \vec{B}$ is:

If $0.5\hat i + 0.8\hat j + {\rm{c\hat k}}$ is a unit vector, then the value of c is

A vector of magnitude 10 units makes an angle of 30° with the x-axis. What is the magnitude of its x-component?

Two vectors $\vec{A}$ and $\vec{B}$ have magnitudes 5 and 12 units, respectively, and the magnitude of their resultant is 13 units. The angle between the vectors is: