Two forces are such that the sum of their magnitudes is $18\; N$ and their resultant is $12\; N$ which is perpendicular to the smaller force. Then the magnitudes of the forces are

A body is moving under the action of two forces ${\vec F_1} = 2\hat i - 5\hat j\,;\,{\vec F_2} = 3\hat i - 4\hat j$. Its velocity will become uniform under an additional third force ${\vec F_3}$ given by

The maximum and minimum magnitude of the resultant of two given vectors are $17 $ units and $7$ unit respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is

Maximum and minimum magnitudes of the resultant of two vectors of magnitudes $P$ and $Q$ are in the ratio $3:1.$ Which of the following relations is true

A truck travelling due north at $20 \,m/s $ turns west and travels at the same speed. The change in its velocity be

The position vectors of points $A, B, C$ and $D$ are $\vec A = 3\hat i + 4\hat j + 5\hat k,\,\vec B = 4\hat i + 5\hat j + 6\hat k,\,\vec C = 7\hat i + 9\hat j + 3\hat k$ and $\vec D = 4\hat i + 6\hat j$ then the displacement vectors $\overrightarrow {AB} $ and $\overrightarrow {CD} $ are