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If the line (x-2)/(3)=(y+1)/(2)=(z-1)/(-...

If the line` (x-2)/(3)=(y+1)/(2)=(z-1)/(-1)` intersects the plane `2x+3y-z+13=0` at a point P and the plane `3x+y+4z=16` at a point Q, then PQ is equla to

A

`sqrt(14)`

B

`2sqrt(7)`

C

14

D

`2sqrt(14)`

Text Solution

Verified by Experts

The correct Answer is:
D
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If the line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the plane 2x+3y-z+13=0 at a point P and the plane 3x+y+4z=16 at a point Q, then PQ is equal to

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Line (x-2)/(-2) = (y+1)/(-3) = (z-5)/1 intersects the plane 3x+4y+z = 3 in the point

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Find the coordinates of the point,where the line (x-2)/(3)=(y+1)/(4)=(z-2)/(2) intersects the plane x-y+z-5=0 .Also find the angle between the line and the plane.

The point of intersection of the line (x)/(1)=(y-1)/(2)=(z+2)/(3) and the plane 2x+3y+z=0 is

MCGROW HILL PUBLICATION-THE DIMENSIONAL GEOMETRY -QUESTIONS FROM PREVIOUS YEARS. AIEEE/JEE MAIN PAPERS
  1. A tetrahedron has vertices P(1,2,1),Q(2,1,3),R(-1,1,2) and O(0,0,0). T...

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  2. Let S be the set of all real values of lamda such that a plane passing...

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  3. If an angle between the line, (x+1)/(2)=(y-2)/(1)=(z-3)/(-2) and the...

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  4. The length of the perpendicular from the point (2, -1, 4) on the strai...

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  5. The equation of a plane containing the line of intersection of the pla...

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  6. Find the equation of the plane through the line of intersection of the...

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  7. If a point R ( 4, y, z ) lies on the line segment joining the poi...

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  8. If the line (x-1)/(2)=(y+1)/(3)=(z-2)/(4) meets the plane, x+2y+3z=15 ...

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  9. A plane passing through the points (0,-1,0) and (0,0,1) and making an ...

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  10. The vertices B and C of a DeltaABC lie on the line, (x+2)/(3)=(y-1)/(0...

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  11. Let A(3,0,-1) ,B(2,10,6) and C(1,2,1) be the vertices of a triangle ...

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  12. A perpendicular is drawn from a point on the line (x-1)/(2)=(y+1)/(-1)...

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  13. If the plane 2x-y+2x+3=0 has the distances (1)/(3) and (2)/(3) units f...

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  14. If the line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the plane 2x+3y-...

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  15. A plane which bisects the angle between the two given planes 2x-y+2z-4...

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  16. Let P be the plane, which contains the line of intersection of the pla...

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  17. if the length of the perpendicular from the point (beta,0,beta ...

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  18. If Q(0, -1, -3) is the image of the point P in the plane 3x-y+4z=2 and...

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  19. The distance of the point having position vector -hati+ 2 hatj + 6 hat...

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  20. The length of the perpendicular drawn from the point (2,1,4) to the pl...

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