Find | a - b | if | a |=3, | b |=4 and a . b =1 - Vidyadip

Question

Find $\big|\vec{\text{a}}-\vec{\text{b}}\big|$ if
$|\vec{\text{a}}|=3,\big|\vec{\text{b}}\big|=4$ and $\vec{\text{a}}.\vec{\text{b}}=1$

✓

Answer

Given that$|\vec{\text{a}}|=3,\big|\vec{\text{b}}\big|=4$ and $\vec{\text{a}}.\vec{\text{b}}=1\dots(1)$
We know that
$\big|\vec{\text{a}}-\vec{\text{b}}\big|^2=|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2-2\vec{\text{a}}.\vec{\text{b}}$
$=3^2+4^2-2(1)$ [using (1)]
$=9+16-2$
$=23$
$\therefore \big|\vec{\text{a}}-\vec{\text{b}}\big|=\sqrt{23}$

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