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Find the cartesian equation of the plane...

Find the cartesian equation of the plane through the point (2,-1, 1) and perpendicular to the vector `4hati+2hatj-3hatk`.

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The correct Answer is:
`4x+2y-3=3`
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Find the vector and cartesian equations of the plane which passes through the point (5, 2, - 4) and perpendicular to the line with direction ratios 2, 3, -1.

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector 3hati+2hatj-2hatk .

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane vecr.(hati+2hatj-5hatk)+9=0

Find the equation of the plane passing through the point (3, 4, -1) and parallel to the plane vecr.(2hati-3hatj+5hatk)+2=0

Find the cartesian equation of the plane| through the intersection of the planes vecr.(2hati+6hatj)+12=0 and vecr.(3hati-hatj+4hatk)=0 which are at a unit distance from the origin.

Find the equation of the plane passing through (a, b, c) and parallel to the plane vecr.(hati+hatj+hatk)=2 .

Find the vector and cartesian equations of the planes : (a) that passes through the point (1, 0, -2) and the normal to the plane is hati+hatj-hatk . (b) that passes through the point (1,4, 6) and the normal vector to the plane is hati-2hatj+hatk .

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

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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK
  1. Find the vector equation of a plane which is at a distance 11 units fr...

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  2. Find the vector equation of the plane vecr=hati-hatj+lambda(hati+hatj+...

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  3. Find the cartesian equation of the plane through the point (2,-1, 1) a...

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

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  5. Find the value of a so that the four points with position vectors -hat...

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  6. A plane meets the co-ordinate axes at A, B and C such that the centroi...

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  7. Show that the plane through (1, 1, 1), (1,-1, 1) and (-7, 3, -5) is pe...

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  8. The foot of perpendicular from the origin to the plane is (4, -2, -5) ...

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  9. Find the equation of the plane passing through the point (-1,2, 1) and...

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  10. Find the equation of the plane containing the line of intersection of ...

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

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  12. Find the equation of the plane passing through the intersection of the...

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  13. Find the cartesian equation of the plane| through the intersection of ...

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  14. Find the equation of the plane passing through the intersection of the...

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  15. In the following cases, determine whether the given planes are paralle...

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  16. If the planes vecr.(hati+2hatj-3hatk)=7 and vecr.(lambdahati+2hatj-7ha...

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  17. Find the distance of the point (2, 1, 0) from the plane 2x + y + 2z + ...

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  18. If the points (1, 1, lambda) and (-3, 0, 1) be equidistant from the pl...

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  19. Find the distance between the parallel planes x + y - z + 4 = 0 and x ...

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  20. Find the distance between the parallel planes vecr.(2hati-3hatj+6hatk...

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