H C Verma Solutions for Chapter: Physics and Mathematics, Exercise 4: EXERCISES

A vector $\overrightarrow{A}$makes an angle of $20°$ and $\overrightarrow{B}$makes an angle of $110°$ with the $x$-axis. The magnitudes of these vectors are $3 \mathrm{m}$and $4 \mathrm{m}$, respectively. Find the resultant.

Let, $\overrightarrow{A}$ and $\overrightarrow{B}$ be the two vectors of magnitude $10 \mathrm{units}$ each. If they are inclined to the $x$-axis at angles $30°$ and $60°$, respectively, find the resultant.

Add vectors $\overrightarrow{A}, \overrightarrow{B}$and $\overrightarrow{C}$, each having magnitude $100 \mathrm{units}$ and inclined to $x$-axis at angles $45°, 135°$ and $315°$ respectively.

Let $\overrightarrow{a}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$and $\overrightarrow{b}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}$. Find the magnitudes of

(a)$\overrightarrow{a}$     (b) $\overrightarrow{b}$
(c) $\overrightarrow{a}+\overrightarrow{b}$ and
(d) $\overrightarrow{a}-\overrightarrow{b}$

Find

$\left(\mathrm{a}\right)$ the magnitude $\left(\mathrm{b}\right)$ $x$ and $y$ components and $\left(\mathrm{c}\right)$ the angle with the $X‐$axis of the resultant of $\overrightarrow{OA}$, $\overrightarrow{BC}$ and $\overrightarrow{DE}$

Two vectors have magnitudes $3 \mathrm{units}$ and $4 \mathrm{units}$ respectively. What should be the angle between them if the magnitude of the resultant is

$\left(\mathrm{a}\right)$ $1 \mathrm{units}$, $\left(\mathrm{b}\right)$ $5 \mathrm{units}$ and $\left(\mathrm{c}\right)$ $7 \mathrm{units}$.

A spy report about a suspected car reads as follows. The car moved $2.00 \mathrm{km}$ towards east, made a perpendicular left turn, ran for $500 \mathrm{m}$, made a perpendicular right turn, ran for $4.00 \mathrm{km}$ and stopped. Find the displacement of the car.

A carrom board ($4 \mathrm{ft}\times 4 \mathrm{ft}$ square) has the queen at the centre. The queen, hit by the striker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen
$\left(\mathrm{a}\right)$ from the centre to the front edge, $\left(\mathrm{b}\right)$ from the front edge to the hole and
$\left(\mathrm{c}\right)$ from the centre to the hole.