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

\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:

Three forces $\vec{F_1} = 2\hat{i} - 3\hat{j}$, $\vec{F_2} = -5\hat{i} + \hat{j}$, and $\vec{F_3} = a\hat{i} + b\hat{j}$ act on a particle. If the particle is in equilibrium, the values of a and b are:

A car travels 3 km east and then 4 km north. What is the magnitude of its displacement from the starting point?

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

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.

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

The angular velocity of a rotating body is $\mathop \omega \limits^ o = 4\,\widehat {\rm{i}}{\rm{ + }}\widehat {\rm{j}}{\rm{ - 2}}\widehat {\rm{k}}$. The linear velocity of the body whose position vector $2\widehat {\rm{i}}{\rm{ + 3}}\widehat {\rm{j}}{\rm{ - 3}}\widehat {\rm{k}}$ is

A plane flies due east at an airspeed of 100 km/h. A wind is blowing from the south at 20 km/h. What is the plane's ground speed?

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?

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: