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If $|\vec{a}|=3,|\vec{b}|=4$ and $|\vec{a}-\vec{b}|=7$, then what is the value of
$|\vec{a}+\vec{b}| ?$
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$|\vec{a}+\vec{b}| ?$
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The correct answer is:
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Given, $|\vec{a}|=3,|\vec{b}|=4$ and $|\vec{a}-\vec{b}|=7$
Since, $|\vec{a}+\vec{b}|^{2}+|\vec{a}-\vec{b}|^{2}=2\left[|\vec{a}|^{2}+|\vec{b}|^{2}\right]$
$\therefore$ By putting the values of $|\vec{a}|,|\vec{b}|$ and $|\vec{a}-\vec{b}|$ we get
$|\vec{a}+\vec{b}|^{2}+7^{2}=2\left[3^{2}+4^{2}\right]$
$|\vec{a}+\vec{b}|^{2}=50-49 \Rightarrow|\vec{a}+\vec{b}|^{2}=1 \Rightarrow|\vec{a}+\vec{b}|=1$
Since, $|\vec{a}+\vec{b}|^{2}+|\vec{a}-\vec{b}|^{2}=2\left[|\vec{a}|^{2}+|\vec{b}|^{2}\right]$
$\therefore$ By putting the values of $|\vec{a}|,|\vec{b}|$ and $|\vec{a}-\vec{b}|$ we get
$|\vec{a}+\vec{b}|^{2}+7^{2}=2\left[3^{2}+4^{2}\right]$
$|\vec{a}+\vec{b}|^{2}=50-49 \Rightarrow|\vec{a}+\vec{b}|^{2}=1 \Rightarrow|\vec{a}+\vec{b}|=1$
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