The distance from the point (3,4,5) to the point where the line 1 x − 3 = 2 y − 4 = 2 z − 5 meets the plane x + y + z = 17 is

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The distance from the point (3,4,5) to the point where the line 1 x − 3 ​ = 2 y − 4 ​ = 2 z − 5 ​ meets the plane x + y + z = 17 is

TestHub · Accepted Answer

Anypoint on the line is ( r + 3 , 2 r + 4 , 2 r + 5 ) . It lies on the plane x + y + z = 17 ∴ ( r + 3 ) + ( 2 r + 4 ) + ( 2 r + 5 ) = 17 i.e r = 1 Thus the point of intersection of the plane and the line is (4,6,7) Required distance = distance between (3,4,5) and (4,6,7) = { ( 4 − 3 ) 2 + ( 6 − 4 ) 2 + ( 7 − 5 ) 2 } ​ = 3

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