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Show that the planes 2x-y+6z=5 and 5x-2....

Show that the planes `2x-y+6z=5` and `5x-2.5y+15z=12` are parallel.

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The given planes are in the form `a_(1)x+b_(1)y+c_(1)z+d_(1)=0` and `a_(2)x+b_(2)y+c_(2)z+d_(2)=0`, where `a_(1)/a_(2)=b_(1)/b_(2)=c_(1)/c_(2)`. Hence, the given planes are parallel.
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RS AGGARWAL-THE PLANE-Exercise 28C
  1. Find the equation of the plane which passes through the point (3,4,-1)...

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  2. Find the equation of the plane mid-parallel to the planes 2x-3y+6z+21=...

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  3. Show that the planes 2x-y+6z=5 and 5x-2.5y+15z=12 are parallel.

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  4. Find the vector equation of the plane through the point (3hati+4hatj-h...

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  5. Find the equation of the plane passing through (a,b,c) and paralle tot...

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  6. Find the vector equation of a plane which is parallel to the plane vec...

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  7. Find the equation of the plane through the point (1,4,-2) and parallel...

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  8. Find the equation of the plane passing through the origin and parallel...

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  9. Find the equation of the plane passing through the point (-1,0,7) and ...

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  10. Find the equations of the planes parallel to the plane x-2y+2z-3=0 whi...

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  11. Find the distance between the planes x+2y+3z+7=0 and 2x+4y+6z+7=0.

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  12. Find the equation of a plane containing the line of intersection of...

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

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  14. Find the equation of the plane passing through the intersection of ...

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  15. Find the equation of the plane passing through the line of intersectio...

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  16. Find the vector equation of the plane passing through the intersection...

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  17. Find the equation of the plane passing through the lineof intersection...

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  18. Find the equation of the plane through the intersection of the planes ...

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  19. Find the vector equation to the plane through the point (2,1,-1) pass...

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  20. Find the vector equation of the plane passing through the point (1,1,1...

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