A and B are two vectors such that their resultant is . . .

Question : A and B are two vectors such that their resultant is perpendicular to A and in magnitude equal to A. The magnitude of vector B is A√n. Then find n.

Doubt by Suhani

Solution : 
ꞵ=90°

R=A
B=A√n

We know, 
tanꞵ=Asinθ/(A+Bcosθ)

tan90°=Asinθ/(A+A√ncosθ) [∵ꞵ=90°, B=A√n]
1/0= Asinθ/[A(1+√ncosθ)]
1/0=sinθ/(1+√ncosθ)
1+√ncosθ =0
√ncosθ =-1
cosθ = -1/√n

Now
R²=A²+B²+2ABcosθ
A²=A²+(A√n)²+2A(A√n)cosθ [∵B=A√n]

A²=A²+A²n+2A²√n(-1/√n] [∵cosθ = -1/√n]
A²=A²+A²n-2A²
A²=A²n-A²
A²+A²=A²n
2A²=A²n
2A²/A²=n
2=n
n=2

Hence, the value of n is 2.

Similar Question : 
The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. The angle between A and B is 

a) 120°

b) 150°

c) 135°

d) 180°

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b) 150°