BM Sharma Solutions for Chapter: Vectors, Exercise 1: DPP

A scooter going due east at $10 \mathrm{m} {\mathrm{s}}^{-1}$ turns right through an angle of $90°$. If the speed of the scooter remains unchanged in taking a turn, the change in the velocity of the scooter is,

A person goes $10 \mathrm{km}$ north and $20 \mathrm{km}$ east. What will be displacement from initial point?

If the resultant of $N$ forces of different magnitudes acting at a point is zero, then the minimum value of $N$ is

A force of $5 \mathrm{N}$ acts on a particle along a direction, making an angle of $60°$ with vertical. Its vertical component will be

$Y$ component of velocity is $20$ and $X$ component of velocity is $10$. The direction of motion of the body with the horizontal at this instant is

A car travels $6 \mathrm{km}$ towards north at an angle of $45°$ to the east and then travels distance of $4 \mathrm{km}$ towards north at an angle of $135°$ to the east. How far is the point from the starting point? What angle does the straight line joining its initial and final position make with the east?

A vector $\overrightarrow{a}$ is turned without a change in its length through a small angle $\text{dθ}$. The value of $\left|\text{∆}\overrightarrow{\mathit{a}}\right|$and $\text{∆}a$ are, respectively,

Find the resultant of three vectors $\overrightarrow{\mathit{O}\mathit{A}}\mathit{,}\overrightarrow{\mathit{ }\mathit{O}\mathit{B}}$ and $\overrightarrow{\mathit{O}\mathit{C}}$ shown in the following figure. Radius of the circle is $R$.