MCQ
If $\left| {\vec a} \right| = 2,\left| {\vec b} \right| = 3$ and $\left| {2\,\vec a - \vec b} \right| = 5$, then $\left| {2\,\vec a + \vec b} \right|$ equals
- A$17$
- B$7$
- ✓$5$
- D$1$
$\sqrt{(2|\vec{a}|)^{2}+|\vec{b}|^{2}-2 \times|2 \vec{a}| \vec{b} | \cos \theta}=5$
Putting values of $|\vec a|$ and $|\vec{b}|,$ we get
$ \Rightarrow (2 \times 2)^{2}+(3)^{2}-24 \cos \theta=25 $
$ \Rightarrow \cos \theta=0$
$ \Rightarrow \quad \theta=\frac{\pi}{2} $
$|2 \vec{a}+\vec{b}|=\sqrt{16+9+24 \cos \theta}=\sqrt{25} $
$=5 $
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