Question

Calculate the scalar product of the following vectors.
What angle do the unit vectors a and b make if the vectors $c=a+2bandd=5a-4b$ are known to be mutually perpendicular?

Answer 1

Two vectors are said to be perpendicular if their scalar product is 0.

given $c.d=0$

$⟹(a+2b).(5a-4b)=0$

$⟹5|a{|}^2-4a.b+10b.a-8|b{|}^2=0$

Given, a and b are unit vectors.

$⟹5+6a.b-8=0$

$⟹a.b=1/2$

If the angle between a and b is $\theta$ then,

$\cos \theta =1/2⟹\theta =\frac{\pi }{3}$