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Find the angle between the planes: vecr....

Find the angle between the planes:
`vecr.(hati+hatj)=1 and vecr.(hati+hatk)=3`.

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The acute angle between the planes vecr.(2hati-3hatj+hatk)=1 and vecr.(hati-2hatj)=2 is………………. .

Find the angle between the planes : vecr*(2hati+2hatj-3hatk)=5 and vecr*(3hati-3hatj+5hatk)=3

Find the acute angle between the planes vecr.(hati+2hatj-hatk)=3 and vecr.(2hati-hatj+2hatk)=2 .

Find the angle between the line vecr=(hati+hatj+hatk)+lambda(2hati-hatj-hatk) and the plane vecr.(hati+hatj-2hatk) =3.

Find the angle between the line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and the plane vecr.(2hati-hatj+hatk)=4 .

Find the angle between the line : vecr=(hati-hatj+hatk)+lambda(2hati-hatj+3hatk) and the plane vecr*(2hati+hatj-hatk)=4 . Also find whether the line is parallel to the plane or not.

Find the angle between the line vecr=(hati-hatj+3hatk)+lambda(2hati-hatj+hatk) and the plane vecr.(hati+hatj+2hatk) =4.

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 equations of the plane through the intersection of the planes vecr.(hati-1hatj)=-6 and vecr.(3hati+3hatj-4hatk)=0 , whose perpendicular distance form the origin is unity.

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Show that the lines (x-a+d)/(alpha-delta) = (y-a)/alpha = (z-a-d)/(alp...

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  2. Find the angle between the planes 2x-3y+4z=1 and -x+y=4.

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  3. Find the angle between the planes: vecr.(hati+hatj)=1 and vecr.(hati+h...

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  4. Find the angle between the two planes 3x-6y+2z = 7 and 2x+2y-2z = 5

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  5. Show that the plane passing through the points (1,1,1), (1,-7,1) and (...

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

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  7. Find the equation of the plane passing through the points (-1,1,1) and...

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  8. Find the equation of the plane passing through the line (x-1)/2=(y+1)/...

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  9. Obtain the equation of the plane passing through the point (1,-3,-2) a...

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  10. Find the angles between the line vecr=-hati+hatj+2hatk+lambda(3hati+2h...

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  11. Find the co-ordinates of the point, where the line: (x-2)/3=(y+1)/4=(z...

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  12. The distance of the point (2,1,-1) from the plane x-2y+4z=9 is :

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  13. Find the distance between the point (7,2,4) and the plane determined b...

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  14. Find the equations of two planes through the point (4,2,1),(2,1,-1) an...

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  15. Find the length of the projection of the line segment joining the poin...

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  16. Show that the line L whose vector equation is vecr=2hati-2hatj+3hatk+l...

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  17. Find the equation of plane passing through the point (1,4,-2) and para...

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  18. Find the equation of the planes parallel to the plane x-2y+2z-3=0 and ...

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  19. The planes 2x-2y+4z+5=0 and 3x-3y+6z-1=0 are

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  20. Find the distance between the parallel planes 2x-y+3z+4=0 and 6x-3y+9z...

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