If | a | = 2, | b | = 3 and | 2 , a - b | = 5, then | 2 , a + b |… - Vidyadip

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
$1$

✓

Answer

Correct option: C.

$5$

c
Given $|2 \vec{a}-\vec{b}|=5$

$\sqrt{(2|\vec{a}|)^{2}+|\vec{b}|^{2}-2 \times|2 \vec{a}| \vec{b} | \cos \theta}=5$

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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