Question

Let a and b be two unit vectors such that $a+2b$ and $5a-4b$ are perpendicular to each other, then the angle between a and b is

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

Answer: (C)

Since, vectors $a+2b$ and $5a-4b$
are perpendicular to each other.
$\therefore$ $(a+2b).(5a-4b)=0$
$\Rightarrow$ $5|a{|}^2+6a.b-8|b{|}^2=0$
$\Rightarrow$ $5{(1)}^2+6a.b-8{(1)}^2=0$
$(\because |a|=|b|=1,given)$
$\Rightarrow$ $6a.b=3$
$\Rightarrow$ $|a||b|\cos \theta =\frac{3}{6}=\frac{1}{2}$
$\Rightarrow$ $1\times 1\times \cos \theta =\frac{1}{2}$
$\Rightarrow$ $\cos \theta =\frac{1}{2}$
$\Rightarrow$ $\theta ={60}^o$