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Find the equation of the plane which bis...

Find the equation of the plane which bisects the line segment joining the points (-1, 2, 3) and (3, -5, 6) at right angles.

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To find the equation of the plane that bisects the line segment joining the points (-1, 2, 3) and (3, -5, 6) at right angles, we can follow these steps: ### Step 1: Find the Midpoint of the Line Segment The midpoint \( M \) of the line segment joining points \( A(-1, 2, 3) \) and \( B(3, -5, 6) \) can be calculated using the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right) \] Substituting the coordinates: ...
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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Show that the normal vector to the plane 2x+2y+2z=3 is equally incline...

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  2. Find a vector of magnitude 26 units normal to the plane 12 x-3y+4z=1.

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  3. Find the equation of the plane which bisects the line segment joining ...

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  4. Find the vector and the Cartesian equation of the plane which pases th...

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  5. If O be the origin and the coordinates of P be(1," "2," "" "3) , th...

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  6. Find the vector equation of a plane at a distance of 5 units from the ...

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  7. Reduce the equation of the plane x-2y-2z=12 to normal form and hence f...

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  8. Find the vector equation of a plane which is at a distance of 6 units ...

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  9. Find the vector equation of a plane which is at a distance of 3 units ...

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  10. Find the vector equation of a plane which is at a distance of 5 units ...

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  11. Reduce the equation 2x-3y-6z=14 to the normal form and hence fine the ...

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  12. Write the normal form of the equation of the plane 2x-3y+6z+14=0.

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  13. The direction ratios of the perpendicular from the origin to a plane ...

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  14. Find a normal vector to the plane x+2y+3z-6=0

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  15. Find the vector equation of the plane which is at a distance of 6/(sq...

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  16. Find the distance of the plane 2x -3y + 4z-6 = 0from the origin.

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  17. Find the vector equation of the plane passing thrugh the points (2,5,-...

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  18. Find the vector equation of the plane passing through the points (1, ...

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  19. Show that the planes 2x+6y-6z=7\ a n d\ 3x+4y+5z=8 are at right angles...

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  20. Find the equation of the plane through the points (2, 1, -1) and (-1, ...

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