Let the line L pass through ( 1 , 1 , 1 ) and intersect the lines 2 x − 1 = 3 y + 1 = 4 z − 1 and 1 x − 3 = 2 y − 4 = 1 z . Then, which of the following points lies on the line L ?

Question

Let the line L pass through ( 1 , 1 , 1 ) and intersect the lines 2 x − 1 ​ = 3 y + 1 ​ = 4 z − 1 ​ and 1 x − 3 ​ = 2 y − 4 ​ = 1 z ​ . Then, which of the following points lies on the line L ?

TestHub · Accepted Answer

​ Dr’s of AC ⇒ 2 λ , 3 λ − 2 , 4 λ Dr’s of BC ⇒ μ + 2 , 2 μ + 3 , μ − 1 ⇒ 2 λ μ + 2 ​ = 3 λ − 2 2 μ + 3 ​ = 4 λ μ − 1 ​ ⇒ 2 ( μ + 2 ) = μ − 1 ⇒ μ = − 5 ⇒ Dr’s of BC ⇒ 3 , 7 , 6 ⇒ equation of L ⇒ 3 x − 1 ​ = 7 y − 1 ​ = 6 z − 1 ​ ​ ( 7 , 15 , 13 ) satisfies.

Mathematics - Vector Question with Solution | TestHub

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