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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.

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The correct Answer is:
x - 2y + 2z - 3 = 0
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Find the vector equation of the plane passing through the intersection of the planes vecr.(hati+hatj+hatk)=6 and vecr.(2hati+3hatj+4hatk)=-5 and the points (1,1,1).

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 equation of the plane through the intersection of the planes vecr.(bari+3barj)-6=0 and barr.(3bari-barj-4bark)=0 , whose perpendicular distance from origin is unity.

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+3hatj-hatk)=0 and vecr.(hatj+2hatk)=0 and also passing through the point 2hati+hatj-hatk .

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr.(hati-hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6

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).

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

Find the equation of the plane which contains the line of intersection of the planes vecr.(hati+2hatj+3hatk)-4=0,vecr.(2hati+hatj-hatk)+5=0 and which is perpendicular to the plane vecr.(5hati+3hatj-6hatk)+8=0

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

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

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK
  1. Find the equation of the plane through the line of intersection of vec...

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

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

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

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

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

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

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

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

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

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  11. If the distance of the plane x - y + z + lambda = 0 from the point (1,...

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  12. The direction cosines of two lines are 1, -2,-2 and 0, 2, 1. Find the ...

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  13. The direction cosines of two lines are given by the following equation...

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  14. Show that the line passing through the points (4, 7, 8) and (2, 3, 4) ...

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  15. Show that the line passing through (1, -1, 2) and (3, 4, -2) is perpen...

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  16. Find the angle between the lines (5-x)/(-2)=(y+3)/(1)=(1-z)/(3) and x/...

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  17. Show that the lines (x-5)/(7)=(y+2)/(-5)=z/1 and x/1=y/2=z/3 are perpe...

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  18. Find the co-ordinates of the point where the line (x+1)/(2)=(y+2)/(3)=...

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  19. Find the co-ordinates of the point where the line through A(3, 4, 1) a...

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  20. Find the coordinates of the foot of perpendicular drawn from the point...

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