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If  are three non-zero vectors with no two of which are collinear,  is collinear with  and  is collinear with , then will be equal to

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  1. Zero
  2. 9
  3. 1
  4. None of the above

Answer (Detailed Solution Below)

Option 1 : Zero
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Detailed Solution

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Cocept:

If a vector A is collinear to other vector B, it can be written as:

 where λ is any scalar number

Calculation:

Given  is collinear with  

⇒  = λ1 ×                       ...(i)

Also given  is collinear with 

⇒  = λ2 ×                      ...(ii)

Subtracting 2×(ii) from (i)

⇒ 

∴ λ1 = - 6, λ2 =  

From (ii)

⇒ = 

⇒ = 

⇒ 

⇒ 

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