A force $\vec{F} = (3\hat{i} + 4\hat{j} - 5\hat{k})$ N acts on a particle causing a displacement $\vec{s} = (2\hat{i} - \hat{j} + 3\hat{k})$ m. The work done by the force 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?

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

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

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

A force $\vec{F} = (6\hat{i} - 8\hat{j} + 10\hat{k})$ N produces an acceleration of $1 ext{ m/s}^2$ in a body. The mass of the body is:

A projectile is launched with an initial velocity of $20 \, m/s$ at an angle of $60^\circ$ with the horizontal. What is the vertical component of its initial velocity?

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 force $\vec{F} = (3\hat{i} + 4\hat{j}) \, N$ acts on a particle. What is the magnitude of the component of this force along the direction $\hat{i} + \hat{j}$?

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

Which of the following represents the vertical component of a vector $\mathbf{V}$ with magnitude $V$ and angle $heta$ with the horizontal?