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Find the equation of the plane passing through the line of intersection of the planes `vecr.(hati+3hatj)-6=0` and `vecr.(3hati-hatj-4hatk)=0`, whose perpendicular distance from the origin is unity.

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The correct Answer is:
`-3`
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Find the Cartesian and vector equation of the planes through the line of intersection of the planes vecr.(hati-hatj)+6=0 and vecr.(3hati+3hatj-4hatk)=0 , which are at a unit distance from the origin.

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+hatj+hatk)=1 and vecr.(2hati+3hatj-hatk)+4=0 and parallel to x-axis.

Find the Cartesian as well as the vector equation of the planes pasing through the intersection of the planes vecr.(2hati=6hatj)+12=0 and vecr.(3hati-hatj+4hatk)=0 which are at unit distance from the origin.

The vector equation of the line of intersection of the planes vecr.(2hati+3hatk)=0 and vecr.(3hati+2hatj+hatk)=0 is

Find the equation of the plane passing through the intersection of the planes vecr.(2hati+hatj+3hatk)=7 , vecr.(2hati+5hatj+3hatk)=9 and the point (2,1,3) .

Find the equation of the plane passing through the intersection of the planes vecr.(2hati+hatj+3hatk)=7, vecr.(2hati+5hatj+3hatk)=9 and the point (3,2,-1) .

The equation of the plane through the intersection of the planes vecr.(2hati+6hatj)+12=0 and vecr.(3hati-hatj+4hatk)=0 and at a unit distance from the origin, is

Find the equation of the plane through the line of intersection of the planes vecr.(2hati-3hatj+4hatk)=1 and vecr.(hati-hatj)+4=0 and perpendicular to the plane vecr.(2hati-hatj+hatk)+8=0 .

Find the vector equation of the plane passing through the intersection of the planes vecr.(hati+hatj+hatk)=6, vecr.(2hati+3hatj+4hatk)=-5 and the point (1,1,1) .

MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY -EXERCISE 11 (E) (LONG ANSWER TYPE QUESTIONS (I) )
  1. (A) Find the equation of the plane through the intersection of the pla...

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  2. Find the vector equation of the following planes in cartesian form : ...

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  3. Find the equations of the plane that passes through three points (1,1,...

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  4. Find the equations of the faces of the tetrahedron whose vertices are ...

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  5. (i) Find the distance of the point P (6,5,9) from the plane determined...

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  6. (i) Find the equation of the plane through the points (2,-3,1) and (5,...

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  7. Find the Cartesian equation of the plane passing through the points...

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  8. (a) show that the following four points are coplanar : (i) (4,5,1), ...

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  9. The foot of the perpendicular drawn from the origin to a plane is (2, ...

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  10. (I) Find the foot and length of the perpendicular from the point (3,4,...

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  11. find the coordinates of point where the line through (3,-4,-5) and (2,...

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  12. If x co-ordinate of a point on the line joining points (2,2,1) and (5,...

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  13. (i) Find the equation of the plane passing through the intersection of...

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  14. (i) Find the vector equation of the plane through the intersection of ...

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

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  16. Find the equation of a plane through the intersection of the planes : ...

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

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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 ...

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  20. (i) Find the equation of the plane passing through (1,-1,2) and perpen...

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