3D Geometry QA 5
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The document discusses a problem regarding the distance between a point (1, 0, 2) and the intersection of a line and a plane defined by the equation x – y + z = 16. The correct answer for the distance, determined through calculations involving parameters of the line and plane, is 13. The content is part of a physics help resource provided by L.K. Satapathy.
3D Geometry QA 5
- 1. Physics Helpline L K Satapathy 3D Geometry QA 5
- 2. Physics Helpline L K Satapathy 3 D Geometry QA 5 Question: The distance of the point ( 1 , 0 , 2 ) from the point of intersection of the line and the plane x – y + z =16 , is ( ) 2 14 ( ) 8 ( ) 3 21 ( ) 13a b c d Answer : 12 2 . . . (1) 3 4 12 yx z 12 2 3 4 12 yx z A(1,0,2) d B L The situation is shown in the figure The given line is L , whose equation is The given plane is , whose equation is 16 . . . (2)x y z Let the given point be A whose coordinates are ( 1 , 0 , 2 ) 12 2 3 4 12 yx zLet Coordinates of any point on the line is (3 2 , 4 1, 12 2)
- 3. Physics Helpline L K Satapathy 3 D Geometry QA 5 Correct option = (d) Since B lies on the plane x – y + z =16 , we have (3 2) (4 1) (12 2) 16 (3 2 , 4 1,12 2) (5 , 3 ,14) 2 2 2 (5 1) (3 0) (14 2)d The required distance between the points ( 1 , 0 , 2 ) and ( 5 , 3 , 14 ) is For some value of , coordinates of B =(3 2 , 4 1, 12 2) Let the point of intersection of the line and the plane be B Coordinates of B 16 9 144 169 13 11 11 1
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