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 $\overrightarrow{a}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$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 mosquito net over a $7 \mathrm{ft}\times 4 \mathrm{ft}$ bed is $3 \mathrm{ft}$ high. The net has a hole at one corner of the bed through which a mosquito enters the net. It flies and sits at the diagonally opposite upper corner of the net.

$\left(\mathrm{a}\right)$ Find the magnitude of the displacement of the mosquito. $\left(\mathrm{b}\right)$ Taking the hole as the origin, the length of the bed as the $X‐$axis, its width as the $Y‐$axis, and vertically up as the $Z‐$axis, write the components of the displacement vector.