Find the equation of the line which is reflection of the line 9 x − 1 = − 1 y − 2 = − 3 z + 3 in the plane 3x − 3 y + 10 z = 26 .

Question

Find the equation of the line which is reflection of the line 9 x − 1 ​ = − 1 y − 2 ​ = − 3 z + 3 ​ in the plane 3x − 3 y + 10 z = 26 .

TestHub · Accepted Answer

The line direction is parallel to the reflecting plane, so reflection preserves it. Reflect one point A to obtain the required line. A = ( 1 , 2 , − 3 ) , d = ( 9 , − 1 , − 3 ) , n = ( 3 , − 3 , 10 ) , n ⋅ d = 0. n ⋅ A − 26 = − 59 , n ⋅ n = 118. A ′ = A − 118 2 ( − 59 ) ​ n = A + n = ( 4 , − 1 , 7 ) . r = ( 4 , − 1 , 7 ) + t ( 9 , − 1 , − 3 ) . ​

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