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Find the distance between the point P(6...

Find the distance between the point `P(6, 5, 9)`and the plane determined by the points `A (3, -1, 2)`, `B (5, 2, 4)`and `C( -1, -1, 6)`.

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`|[(x-x_1),(y-y_1),(z-z_1)],[(x_2-x_1),(y_2-y_1),(z_2-z_1)]|`
`|[x-x_1,y-y_1,z-z_1],[x_2-x_1,y_2-y_1,z_2-z_1],[x_3-x_1,y_3-y_1,z_3-z_1]|`
The plane is passing through points `A (x_1, y_1, z_1)`, `B (x_2, y_2, z_2)` and `C (x_3, y_3, z_3)`
`|[x-x_1,y-y_1,z-z_1],[x_2-x_1,y_2-y_1,z_2-z_1],[x_3-x_1,y_3-y_1,z_3-z_1]|`
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Find the distance between the points P(-6,-3) and Q(-1,9) .

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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Prove that if a plane has the intercepts a, b, c and is at a distance...

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  2. If the points (1,\ 1,\ lambda)a n d\ (-3,\ 0,\ 1) be equidistant from ...

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  3. Find the distance between the point P(6, 5, 9)and the plane determine...

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  4. Find the equation of a plane passing through the pint P(6,\ 5,\ 9) and...

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  5. A variable plane is at a constant distance p from the origin and meets...

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  6. A variable plane at a constant distance p from the origin meets the co...

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  7. Find the distance of the point 2 hat i- hat j-4 hat k from the plane ...

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  8. Find the distance of the point (2, 3, -5) from the plane x+2y-2z-9=0.

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  9. Show that the points (1, 1, 1) and (-3, 0, 1) are equidistant from the...

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

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  11. Find the distance of the point (2, 3, 5) from the xy-plane.

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  12. If the product of distances of the point (1,1,1) from the origin and p...

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  13. Find the distance between the point (7,2,4) and the plane determined b...

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  14. Find the distance between the planes 2x-y+2z=4 and 6x-3y+6z=2.

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  15. Prove that the four points having position vectors are non-coplanar: ...

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  16. Find the equation of the plane mid parallel to the planes 2x-2y+z+3=0\...

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  17. Reduce the equation of line x-y+2z=5a d n3x+y+z=6 in symmetrical fo...

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

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

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

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