Two vectors a and b are such that |a+b|=|a-b| . . .

Question : Two vectors a and b are such that |a+b|=|a-b|, the angle between a and b in degree is 15x.

Doubt by Suhani

Solution :

θ=15x — (1)

|a+b|=|a-b| (Given)

R²=R'²
a²+b²+2abcosθ=a²+b²-2abcosθ
2abcosθ=-2abcosθ
2abcosθ+2abcosθ=0
4abcosθ=0
cosθ=0
cosθ=cos90°

θ=90° — (2)

From equation (1) and (2)

15x=90

x=90/15

x=6

Hence, the required value of x is 6.

Similar Question :

Two vectors A and B are such that |A+B|=|A-B|. The angle between the vectors A and B is

(a) 0°

(b) 60°

(d) 180°