Kinematics 6 Question 2

2. Two vectors A and B have equal magnitudes. The magnitude of (A+B) is ’ n ’ times the magnitude of (AB). The angle between A and B is

(2019 Main, 10 Jan II)

(a) sin1n21n2+1

(b) sin1n1n+1

(c) cos1n21n2+1

(d) cos1n1n+1

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Answer:

Correct Answer: 2. (c)

Solution:

  1. Given, |A|=∣B

 or A=B

Let magnitude of (A+B) is R and for (AB) is R.

Now, R=A+B

and R2=A2+B2+2ABcosθ

R2=2A2+2A2cosθ

 Again, R=ABR2=A2+B22ABcosθR2=2A22A2cosθ

[ using Eq. (i) ]

Given,

R=nR or RR2=n2

Dividing Eq. (ii) with Eq. (iii), we get

n21=1+cosθ1cosθ

 or n21n2+1=(1+cosθ)(1cosθ)(1+cosθ)+(1cosθ)n21n2+1=2cosθ2=cosθ or θ=cos1n21n2+1



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