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The equation of the plane passing throug...

The equation of the plane passing through the intersection of `x + 2y + 3x + 4 = 0 and 4x + 3y + 2z+ 1 = 0` and the origin `(0.0, 0)` is

A

`x+y+z=0`

B

`3x+2y+z+1=0`

C

`2x+3y+z=0`

D

`3x+2y+z=0`

Text Solution

Verified by Experts

The correct Answer is:
a
Any plane through the given planes is
`" "x+2y+3z-4+lamda(4x+3y + 2z +1)=0`
It passes through `(0, 0, 0)`. Therefore,
`" "-4+lamda=0`
or `" "lamda=4`
Therefore, the required plane is `x+2y+3z+4(4x+3y+2z)=0 or 17x+ 14y+ 11z=0`.
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
  1. The three planes 4y+6z=5,2x+3y+5z=5a n d6x+5y+9z=10 a. meet in a poi...

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  2. The equation of the plane through the line of intersection of the plan...

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  3. Equation of the pane passing through the points (2,2,1)a n d(9,3,6),...

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  4. Value of lamda such that the line (x-1)/(2)=(y-1)/(3)=(z-1)/(lamda) is...

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  5. The equation of the plane passing through the intersection of x + 2y +...

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  6. The plane 4x+7y+4z+81=0 is rotated through a right angle about its ...

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  7. The vector equation of the plane passing through the origin and the li...

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  8. The two lines vecr=veca+veclamda(vecbxxvecc) and vecr=vecb+mu(veccxxve...

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  9. The projection of the line (x+1)/(-1)=y/2=(z-1)/3 on the plane x-2y+z=...

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  10. The direction cosines of a line satisfy the relations lambda(l+m)=n ...

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  11. The line through the points (-2, a) and (9, 3)has slope (-1)/(2). Find...

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  12. Find the angle between the lines whose direction cosines are given by ...

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  13. A sphere of constant radius 2k passes through the origin and meets ...

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  14. A plane passes through a fixed point (a ,b ,c)dot The locus of the ...

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  15. What is the nature of the intersection of the set of planes x+a y+(...

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  16. Find the equation of a straight line in the plane vecr.vecn=d which is...

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  17. What is the equation of the plane which passes through the z-axis and ...

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  18. A straight line L on the xy-plane bisects the angle between O Xa n dO ...

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  19. For what value (s) of a will the two points (1,a ,1)a n d(-3,0,a) l...

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  20. If the plane x/2+y/3+z/6=1 cuts the axes of coordinates at points, A ,...

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