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Question Number 28695 by yesaditya22@gmail.com last updated on 29/Jan/18

$$\mid \overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}\mid =40,\mid \overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}\mid =20\mathrm{\&}\mid \overrightarrow{\mathrm{a}}\mid =10\mathrm{then}\mathrm{find}\mid \overrightarrow{\mathrm{b}}\mid$$

Answered by mrW2 last updated on 29/Jan/18

$${40}^2=a^2+b^2-2ab\cos \theta$$ $${20}^2=a^2+b^2-2ab\cos (180-\theta )$$ $${20}^2=a^2+b^2+2ab\cos \theta$$ $$b^2=\frac{{40}^2+{20}^2}{2}-a^2=\frac{{40}^2+{20}^2}{2}-{10}^2=900$$ $$\Rightarrow b=\sqrt{900}=30$$

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