Question

PLEASE HELP. PROPER ANSWERS ONLY
if vectors a+2b and 5a-4b are perpendicular to each other and a and b are unit vectors. Find the angle between a and b.

Answer 1

Answer:

HELLO THERE,

let A vector = a+2b

let B vector = 5a-4b

A.B = 0

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

expanding , a.5a - 4 a.b + 10 a.b - 8 b.b=0

since a.a and b.b = 1, ( bcoz a.a = 1.1.cos0)

5-8 + 6 a.b = 0

a.b = 1/2

ab cos(theta) = 1/2

THEREFORE, THETA = 60degrees or pi/3 radians.

the key in the question is the expansion because dot product follows distributive law