Let P ( α , β , γ ) be the image of the point Q ( 1 , 6 , 4 ) in the line 1 x = 2 y − 1 = 3 z − 2 . Then 2 α + β + γ is equal to_______

Question

Let P ( α , β , γ ) be the image of the point Q ( 1 , 6 , 4 ) in the line 1 x ​ = 2 y − 1 ​ = 3 z − 2 ​ . Then 2 α + β + γ is equal to_______

TestHub · Accepted Answer

​ A ( t , 2 t + 1 , 3 t + 2 ) QA ​ = ( t − 1 ) i ^ + ( 2 t − 5 ) j ^ ​ + ( 3 t − 2 ) k ^ QA ​ ⋅ b = 0 ( t − 1 ) + 2 ( 2 t − 5 ) + 3 ( 3 t − 2 ) = 0 14 t = 17 α = 14 20 ​ β = 14 12 ​ γ = 14 102 ​ 2 α + β + γ = 14 154 ​ = 11 ​

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