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The equation of the plane containing ...

The equation of the plane containing the line `2x-5y""+""z""=""3;""x""+""y""+""4z""=""5` , and parallel to the plane, `x""+""3y""+""6z""=""1` , is : (1) `2x""+""6y""+""12 z""=""13` (2) `x""+""3y""+""6z""=-7` (3) `x""+""3y""+""6z""=""7` (4) `2x""+""6y""+""12 z""=-13`

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To find the equation of the plane that contains the given line and is parallel to the specified plane, we can follow these steps: ### Step 1: Identify the equations of the lines The equations of the lines given are: 1. \( 2x - 5y + z = 3 \) 2. \( x + y + 4z = 5 \) ### Step 2: Solve the equations for a point on the line ...
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JEE MAINS PREVIOUS YEAR-THREE DIMENSIONAL GEOMETRY-All Questions
  1. If a line makes an angle of pi/4 with the positive directions of ea...

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  2. The line passing through the points (5, 1, a) and (3, b, 1) crosses...

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  3. If straight lines (x-1)/k=(y-2)/2=(z-3)/3 and (x-2)/3=(y-3)/k=(z-1)/2 ...

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  4. Let the line (x-2)/3=(y-1)/(-5)=(z+2)/2 lie in the plane x""+""3y"...

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  5. Statement-1: The point A(3, 1, 6) is the mirror image of the poi...

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  6. A line AB in three-dimensional space makes angles 45^o and 120^o wi...

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  7. Statement-1 : The point A(1, 0, 7) is the mirror image of the point B(...

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  8. If the angle between the line x=(y-1)/2=(z-3)/lambda and the plane ...

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  9. An equation of a plane parallel to the plane x""""2y""+""2z""""5""=""0...

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  10. If the lines (x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-k)/2=z/1 intersec...

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  11. Distance between two parallel planes 2x""+""y""+""2z""=""8 and 4x"...

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  12. If the lines (x-2)/1=(y-3)/1=(x-4)/(-k) and (x-1)/k=(y-4)/2=(x-5)/1 a...

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  13. The angle between the lines whose direction cosines satisfy the equ...

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  14. The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+...

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  15. The equation of the plane containing the line 2x-5y""+""z""=""3;""x...

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  16. The distance of the point (1, 0, 2) from the point of intersection ...

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  17. The distance of the point (1,-5,""9) from the plane x-y+z=5 measured a...

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  18. If the line, (x-3)/2=(y+2)/(-1)=(z+4)/3 lies in the plane, l x+m y-z=9...

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  19. If the image of the point P(1,-2,3) in the plane, 2x+3y-4z+22=0 measur...

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  20. The distance of the point (1,3,-7) from the plane passing through the ...

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