Find | a - b | if | a |=2, | b |=3 and a . b =4 - Vidyadip

Question

Find $\big|\vec{\text{a}}-\vec{\text{b}}\big|$ if
$|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=3$ and $\vec{\text{a}}.\vec{\text{b}}=4$

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Answer

Given that$|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=3$ and $\vec{\text{a}}.\vec{\text{b}}=4\dots(1)$
We know that
$\big|\vec{\text{a}}-\vec{\text{b}}\big|^2=|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2-2\vec{\text{a}}.\vec{\text{b}}$
$=2^2+3^2-2(4)$ [using (1)]
$=4+9-8$
$=5$
$\therefore \big|\vec{\text{a}}-\vec{\text{b}}\big|=\sqrt{5}$

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