3D Geometry QA 9
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The document presents a problem involving 3D geometry, where the intersection of a line joining points q(2,3,5) and r(1,-1,4) with the plane 5x-4y-z=1 is calculated, along with the foot of the perpendicular from point t(2,1,4) to line qr. It includes a detailed breakdown of the mathematical equations and coordinates involved, ultimately leading to the length of the line segment ps being derived as 1. The correct option for the problem is indicated as (a).
![Physics Helpline
L K Satapathy
3 D Geometry QA 9
(2,3,5)Q
(1, 1,4)R
P
S
(2,1,4)T
For some value of , coordinates of S ( 1,4 1, 4)
DRs of TS ( 1 2,4 1 1, 4 4) ( 1,4 2, )
And DRs of QR (1,4,1)
PR TS 1( 1) 4(4 2) 1( ) 0
118 9 0
2
Coordinates of S 3 9( 1,4 1, 4) , 1,
2 2
2 2 2
4 3 1 13 91
3 2 3 3 2
PS
1 4 1 1 16 1 1
36 9 36 36 2
[ ]Ans
Correct option = (a)](https://image.slidesharecdn.com/qa9-160510100819/85/3D-Geometry-QA-9-3-320.jpg)
3D Geometry QA 9
- 1. Physics Helpline L K Satapathy 3D Geometry QA 9
- 2. Physics Helpline L K Satapathy 3 D Geometry QA 9 Question: Let P be the point of intersection of the straight line joining the points Answer : Q (2,3,5) and R (1 , –1 , 4) with the plane 5x – 4y – z = 1 . If S be the foot of the perpendicular dropped from the point T (2,1,4) on QR , then the length of the line segment PS is 1( ) ( ) 2 ( ) 2 ( ) 2 2 2 a b c d Equation of QR is 11 4 2 1 3 1 5 4 yx z 11 4 . . . (1) 1 4 1 yx z Any point on QR ( 1,4 1, 4) If it lies on plane, then 5( 1) 4(4 1) 1( 4) 1 112 5 1 3 4 1 13( 1,4 1, 4) , , 3 3 3 P (2,3,5)Q (1, 1,4)R P S (2,1,4)T
- 3. Physics Helpline L K Satapathy 3 D Geometry QA 9 (2,3,5)Q (1, 1,4)R P S (2,1,4)T For some value of , coordinates of S ( 1,4 1, 4) DRs of TS ( 1 2,4 1 1, 4 4) ( 1,4 2, ) And DRs of QR (1,4,1) PR TS 1( 1) 4(4 2) 1( ) 0 118 9 0 2 Coordinates of S 3 9( 1,4 1, 4) , 1, 2 2 2 2 2 4 3 1 13 91 3 2 3 3 2 PS 1 4 1 1 16 1 1 36 9 36 36 2 [ ]Ans Correct option = (a)
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