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The sum of two vectors  and  is a vector  such that . Then, find the angle between  and .

  1. 160° 
  2. 120° 
  3. 60° 
  4. 135° 

Answer (Detailed Solution Below)

Option 2 : 120° 
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Detailed Solution

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Concept:

Dot Product of two vectors  and  is defined as , where  is the magnitude of vector .

.

Calculation:

We are given that "sum of two vectors  and  is a vector ".

⇒ 

Taking dot product of both sides with themselves, the magnitudes will still be equal:

⇒ 

⇒ 

Since , we get:

⇒ 

⇒ 

⇒ 

⇒ 

⇒ |b|.|c|.cosθ = 

⇒ 4.4.cosθ = 

⇒ 

⇒ θ = 120° 

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