If  and are collinear vectors, then what are the possible values of p and q respectively?

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  1. 4, 1
  2. 1, 4

Answer (Detailed Solution Below)

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Concept:

For two vectors  to be collinear,​  where λ is a scalar.

Calculation:

Given that, the vectors  &  are collinear.

Since two vectors  are collinear then  where λ is a scalar.

⇒ 

⇒ 

⇒ λp = 4,  λq = 1 and -2λ = -3

⇒  λ = 3/2 

So, by substituting λ = 3/2 in  λp = 4 and λq = 1, we get

⇒ (3/2)p = 4 and (3/2)q = 1

⇒ p = 8/3 and q  = 2/3

∴  is the correct answer.

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