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If the axes are rectangular and `P` is the point (2, 3, -1), find the equation of the plane through `P` at right angle to `O Pdot`

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To find the equation of the plane through the point \( P(2, 3, -1) \) that is perpendicular to the vector \( \overrightarrow{OP} \), we can follow these steps: ### Step 1: Identify the point and the vector The point \( P \) is given as \( (2, 3, -1) \). The origin \( O \) is at \( (0, 0, 0) \). The vector \( \overrightarrow{OP} \) can be calculated as: \[ \overrightarrow{OP} = P - O = (2 - 0, 3 - 0, -1 - 0) = (2, 3, -1) \] ...
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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. The coordinate of the foot of the perpendicular drawn from  the origin...

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  2. Find the equation of the plane passing through the point (2,3,1) ha...

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  3. If the axes are rectangular and P is the point (2, 3, -1), find the eq...

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  4. Find the intercepts made on the coordinate axes by the plane 2x+y-2z=3...

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  5. Find the equation of the plane that bisects the line segment joining ...

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  6. Show that the normal to the following planes are perpendicular to each...

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  7. Show that the normal to the following planes are perpendicular to each...

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  8. Show that the equation of the planes are perpendicular to each other. ...

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  9. Show that the normal vector to the plane 2x+2y+2z=3 is equally incline...

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

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

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

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

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

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

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

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

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

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

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

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