If | a|=2, | b|=3 and |2 a- b|=5, then |2 a+ b| equals:

Question

Accepted Answer

$|2\vec a-\vec b|^2=4|\vec a|^2+|\vec b|^2-4\vec a\cdot\vec b=25 \implies 16+9-4\vec a\cdot\vec b=25 \implies \vec a\cdot\vec b=0$

$$|2\vec a+\vec b|^2=4|\vec a|^2+|\vec b|^2+4\vec a\cdot\vec b=16+9+0=25 \implies |2\vec a+\vec b|=5$$

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