91Ó°ÊÓ

It is given that $\stackrel{→}{E}=2\hat{i}+3\hat{j}and\stackrel{→}{F}=2\hat{i}-2\hat{j}.$We need to determine the magnitude of $E$and$F.$

$\stackrel{→}{E}=2\hat{i}+3\hat{j}.$

$E_x=2and{E}_y=3.$

$\left|\stackrel{→}{E}\right|=\sqrt{{\left(E_x\right)}^2+{\left(E_y\right)}^2}.$

$=\sqrt{{\left(2\right)}^2+{\left(3\right)}^2}.$

$=\sqrt{4+9}.$

$=\sqrt{13}.$

$\stackrel{→}{F}=2\hat{i}-2\hat{j}.$

$F_x=2,F_y=-2.$

$\left|\stackrel{→}{F}\right|=\sqrt{{\left(F_x\right)}^2+{\left(F_y\right)}^2}.$

$=\sqrt{{\left(2\right)}^2+{\left(-2\right)}^2}.$

$=\sqrt{4+4}.$

$=\sqrt{8}.$

It is given that,$\stackrel{→}{E}=2\hat{i}+3\hat{j}and\stackrel{→}{F}=2\hat{i}-2\hat{j}.$We need to determine the magnitude of$\stackrel{→}{E}+\stackrel{→}{F}.$

$\stackrel{→}{E}=2\hat{i}+3\hat{j}and\stackrel{→}{F}=2\hat{i}-2\hat{j}.$

$\stackrel{→}{E}+\stackrel{→}{F}=\left(2\hat{i}+3\hat{j}\right)+\left(2\hat{i}-2\hat{j}.\right)$

$=4\hat{i}-\hat{j}.$

role="math" localid="1649179077562" ${\left(E+F\right)}_x=4,{\left(E+F\right)}_y=-1.$

$\left|\stackrel{→}{E}+\stackrel{→}{F}\right|=\sqrt{{\left(E+F\right)}_x^2+{\left(E+F\right)}_y^2}.$

$=\sqrt{{\left(4\right)}^2+{\left(-1\right)}^2.}$

$=\sqrt{16+1}.$

$=\sqrt{17}.$

It is given that, $\stackrel{→}{E}=2\hat{i}+3\hat{j}and\stackrel{→}{F}=2\hat{i}-2\hat{j}.$We need to determine the magnitude of$-\stackrel{→}{E}+2\stackrel{→}{F}.$

$\stackrel{→}{E}=2\hat{i}+3\hat{j}and\stackrel{→}{F}=2\hat{i}-2\hat{j}.$

$-\stackrel{→}{E}-2\stackrel{→}{F}.$

$=-\left(2\hat{i}+3\hat{j}\right)-2\left(2\hat{i}-2\hat{j}\right).$

$=-2\hat{i}-3\hat{j}-4\hat{i}+4\hat{j}.$

$=-6\hat{i}+\hat{j}.$

${\left(-E+2F\right)}_x=-6,{\left(-E+2F\right)}_y=1.$

$\left|-\stackrel{→}{E}+2\stackrel{→}{F}\right|=\sqrt{{{\left(-E+2F\right)}^2}_x+{{\left(-E+2F\right)}^2}_y}.$

$=\sqrt{{\left(-6\right)}^2+{\left(1\right)}^2.}$

$=\sqrt{36+1}.$

$=\sqrt{37}.$