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Find the equation of the plane through the line of intersection of the planes `x+2y+3z+4=0\ a n d\ x-y+z+3=0` and passing through the origin.

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To find the equation of the plane through the line of intersection of the planes \( x + 2y + 3z + 4 = 0 \) and \( x - y + z + 3 = 0 \), and passing through the origin, we can follow these steps: ### Step 1: Write the equations of the given planes The equations of the two planes are: 1. Plane 1: \( P_1: x + 2y + 3z + 4 = 0 \) 2. Plane 2: \( P_2: x - y + z + 3 = 0 \) ### Step 2: Form the equation of the family of planes ...
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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Find the equation of the plane through the point 2 hat i+ hat j- hat k...

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  2. Find the equation of the plane passing through the line intersection o...

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

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  4. Find the vector equation (in scalar product form) of the plane cont...

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  5. Find the equation of the plane which is perpendicular to the plane 5x+...

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

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

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

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  9. Prove that if a plane has the intercepts a, b, c and is at a distance...

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

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

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

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

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

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

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

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

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

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

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

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