Find | a - b | if | a |=2, | b |=5 and a . b =8 - Vidyadip

Question

Find $\big|\vec{\text{a}}-\vec{\text{b}}\big|$ if
$|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=5$ and $\vec{\text{a}}.\vec{\text{b}}=8$

✓

Answer

Given that$|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=5$ and $\vec{\text{a}}.\vec{\text{b}}=8\dots(1)$
We know that
$\big|\vec{\text{a}}-\vec{\text{b}}\big|^2=|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2-2\vec{\text{a}}.\vec{\text{b}}$
$=2^2+5^2-2(8)$ [using (1)]
$=4+25-16$
$=13$
$\therefore \big|\vec{\text{a}}-\vec{\text{b}}\big|=\sqrt{13}$

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