Question

If a+b+c=0 and |a|=3, |b|=4 and $|c|=\sqrt{37}$, the angle between a and b is

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{3}$

Answer 1

The correct option is D $\frac{\pi }{3}$

$a+b+c=0\Rightarrow a+b=-c\Rightarrow |a+b{|}^2=|c{|}^2\Rightarrow |a{|}^2+|b{|}^2+2a.b=|c{|}^2\Rightarrow 9+16+2\left(3\right)\left(4\right)cos(a,b)=37\Rightarrow 24cos(a,b)=12\Rightarrow cos(a,b)=\frac{1}{2}\Rightarrow (a,b)=\frac{\pi }{3}$