A particle is simultaneously acted by two forces equal to $4\, N$ and $3 \,N$. The net force on the particle is

A passenger arriving in a new town wishes to go from the station to a hotel located $10 \;km$ away on a straight road from the station. A dishonest cabman takes him along a circuitous path $23\; km$ long and reaches the hotel in $28 \;min$. What is

$(a)$ the average speed of the taxi,

$(b)$ the magnitude of average velocity ? Are the two equal ?

On an open ground, a motorist follows a track that turns to his left by an angle of $60^{°}$ after every $500\; m$. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.

Three forces given by vectors $2 \hat{i}+2 \hat{j}, 2 \hat{i}-2 \hat{j}$ and $-4 \hat{i}$ are acting together on a point object at rest. The object moves along the direction

The magnitudes of vectors $\vec A,\,\vec B$ and $\vec C$ are $3, 4$ and $5$ units respectively. If $\vec A + \vec B = \vec C$, the angle between $\vec A$ and $\vec B$ is

A particle is situated at the origin of a coordinate system. The following forces begin to act on the particle simultaneously (Assuming particle is initially at rest)

${\vec F_1} = 5\hat i - 5\hat j + 5\hat k$            ${\vec F_2} = 2\hat i + 8\hat j + 6\hat k$

${\vec F_3} =  - 6\hat i + 4\hat j - 7\hat k$         ${\vec F_4} =  - \hat i - 3\hat j - 2\hat k$

Then the particle will move