Let A be a point on the line r ˉ = ( − 3 i ^ + 6 j ^ + 3 k ^ ) + t ( 2 i ^ + 3 j ^ − 2 k ^ ) and B be a point on the line r ˉ = 6 j ^ + s ( 2 i ^ + 2 j ^ − k ^ ) . The least value of the dista

Question

Let A be a point on the line r ˉ = ( − 3 i ^ + 6 j ^ ​ + 3 k ^ ) + t ( 2 i ^ + 3 j ^ ​ − 2 k ^ ) and B be a point on the line r ˉ = 6 j ^ ​ + s ( 2 i ^ + 2 j ^ ​ − k ^ ) . The least value of the distance AB is

TestHub · Accepted Answer

Let A o ​ = ( − 3 , 6 , 3 ) , B o ​ = ( 0 , 6 , 0 ) ; c ˉ = ( 2 , 3 , − 2 ) & d ˉ = ( 2 , 2 , − 1 ) Then AB m i n ​ =∣ proj of A O ​ B o ​ ​ on c × d ​ = 3 ∣ ( 3 , 0 , − 3 ) ⋅ ( 1 , − 2 , − 2 ) ∣ ​ = 3

Mathematics - Vector Question with Solution | TestHub

Doubts & Discussion

JEE Main (2026)