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Find the equation of the plane passing through the line of intersection of the planes `2x-7y+4z-3=0,\ 3x-5y+4z+11=0\ ` and the point`\ (-2,\ 1,\ 3)dot`

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To find the equation of the plane passing through the line of intersection of the given planes and the point (-2, 1, 3), we can follow these steps: ### Step 1: Identify the equations of the given planes The equations of the two planes are: 1. \( P_1: 2x - 7y + 4z - 3 = 0 \) 2. \( P_2: 3x - 5y + 4z + 11 = 0 \) ### Step 2: Form the equation of the family of planes ...
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If the eqution of the plane passing through the line of intersection of planes 2x - 7y + 4z -3 =0, 3x - 5y + 4z + 11 =0 and the point ( -2,1,3) at ax + by +cz -7=0 , then the value of 2a +b +c -7 is "____________" .

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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Find the equation of the plane which is parallel to 2x-3y+z=0 and whic...

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  2. Find the equation of the plane through (3, 4, -1) which is parallel to...

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

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  4. Find the equation of the plane through the point 2 hat i+ hat j- hat k...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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