Question

Let a and b be two unit vectors. If the vectors c=a+2b and d=5a-4b are perpendicular to each other, then the angle between a and b is

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

Answer 1

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

$(c,d)=\frac{\pi }{2}\Rightarrow c.d=0$
$\Rightarrow (a+2b).(5a-4a)=0\Rightarrow 5a.a-4a.b+10b.a-8b.b=0\Rightarrow 5+6a.b-8=0\Rightarrow a.b=\frac{1}{2}\Rightarrow cos(a,b)=\frac{1}{2}\Rightarrow (a,b)=\frac{\pi }{3}$