If | a |=2, | b |=5 and a . b =2, find | a - b |. - Vidyadip

Question

If $|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=5$ and $\vec{\text{a}}.\vec{\text{b}}=2,$ find $\big|\hat{\text{a}}-\hat{\text{b}}\big|.$

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Answer

We have $|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=5$ and $\vec{\text{a}}.\vec{\text{b}}=2$
Now,$\big|\hat{\text{a}}-\hat{\text{b}}\big|^2=|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2-2\vec{\text{a}}.\vec{\text{b}}$
$=2^2+5^2-2(2)$
$=4+25-4$
$=25$
$\therefore\big|\vec{\text{a}}-\vec{\text{b}}\big|=\sqrt{25}=5$

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