Question

If $a+b+c=0$ and $|a|=3;|b|=5;|c|=7$, find the angle between a vector and b

• A. ${60}^0$
• B. ${30}^0$
• C. ${45}^0$
• D. $noneofthese$

Answer 1

The correct option is A ${60}^0$

$|a|=3,|b|=4,|c|=5$

$a+b+c=0$

$⟹a+b=-c$

$⟹|a+b|=|-c|$

$⟹|a+b{|}^2=|-c{|}^2$

$⟹|a{|}^2+|b{|}^2+2a.b=|c{|}^2$

$⟹9+25+2a.b=49$

Also $ab=3\times 5$

Hence $9+25+2ab\cos \theta =49$

$⟹15=30\cos \theta$

Or $\cos \theta =\frac{1}{2}$

$\theta ={60}^0$

so angle is ${60}^0$.