Let R be the relation over the set of all straight lines in a plane such that ℓ1 R ℓ2⬄ ℓ1⊥ ℓ2. Then, R is

Think of line as a vector quantity:

As ℓ1⊥ ℓ2;


And ℓ2⊥ ℓ1


Hence R is symmetric.


Also Given a relation R over straight lines such that ℓ1⊥ ℓ2


As ℓ1⊥ ℓ2:


⇒ ℓ1. ℓ2=0(DOT PRODUCT)


∵ cos θ =0 as θ =90°;


⇒ This thing is possible if ℓ1 and ℓ2 are symmetric.


E.g. A= 2i-4j and B=-4i-2j


⇒ A. B=-8+8=0

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