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If  are two vectors such that  then which one of the following is correct?

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  1.  must be unit vectors.
  2.  must be parallel to 
  3.  must be perpendicular to 
  4.  must be equal to 

Answer (Detailed Solution Below)

Option 3 :  must be perpendicular to 
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Detailed Solution

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CONCEPT:

The scalar product of two vectors is given by 

If the vectors  are perpendicular then 

CALCULATION:

Given:  are two vectors such that 

⇒ 

⇒ 

⇒ 

∵ 

⇒ 

⇒ 

⇒ 

So,  must be perpendicular to 

Hence, correct option is 3.

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