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# Solve the following

Question:

Let $\vec{a}=4 \hat{\imath}+3 \hat{\jmath}$ and $\vec{b}=3 \hat{\imath}+4 \hat{\jmath}$. (a) Find the magnitudes of (a) $\vec{a}$, (b) $\vec{b}$, (c) $\vec{a}+\vec{b}$ and (d) $\vec{a}-\vec{b}$.

Solution:

$a=4 i+3 j, b=3 i+4 j$

$|a|=|b|=\sqrt{\left(3^{2}+4^{2}\right)}=5$

$a+b=7 i+7 j$ and $a-b=i-j$

$|a+b|$

$=\sqrt{\left(7^{2}+7^{2}\right)}=7 \sqrt{2}$ and $|a-b|=\sqrt{\left(1^{2}+1^{2}\right)}=\sqrt{2}$