Question

Vectors a cap+2b cap and 5 a cap -4 b cap are mutually perpendicular then the angle between a and b

Answer 1

Answer:

As the two vectors are perpendicular,

Their dot product is zero

(a+2b)(5a-4b)=0

5a^2+6abcos(theta)-8b^2=0 (costheta is angle between acap and bcap)

As you mentioned acap and bcap, it means that they are unit vectors and have magnitude 1.

5+6costheta-8=0

Costheta=3/6=1/2

Theta=pi/3 or 60 degrees