If the image of the point ( 4 , 4 , 3 ) in the line 2 x − 1 = 1 y − 2 = 3 z − 1 is ( α , β , γ ) , then α + β + γ is equal to

Question

If the image of the point ( 4 , 4 , 3 ) in the line 2 x − 1 ​ = 1 y − 2 ​ = 3 z − 1 ​ is ( α , β , γ ) , then α + β + γ is equal to

TestHub · Accepted Answer

Let coordinate of R = ( 2 r + 1 , r + 2 , 3 r + 1 ) ∵ PR is perpendicular to given line. ∴ ( 2 r − 3 ) ⋅ 2 + ( r − 2 ) ⋅ 1 + ( 3 r − 2 ) ⋅ 3 = 0 ∴ r = 1 ∴ Coordinate of R = ( 3 , 3 , 4 ) ∴ ( α , β , γ ) = ( 2 , 2 , 5 ) ∴ α + β + γ = 9

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