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Find the angles between the line vecr=-h...

Find the angles between the line `vecr=-hati+hatj+2hatk+lambda(3hati+2hatj+4hatk)` and the plane `vecr.(2hati+hatj-3hatk)+4=0`

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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-hatk) and the plane vecr.(hati+hatj-2hatk) =3.

Find the angle between the line vecr=(hati-hatj+3hatk)+lambda(2hati-hatj+hatk) and the plane vecr.(hati+hatj+2hatk) =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 : (2hati+3hatj+4hatk)+lambda(2hati+3hatj+4hatk) and the plane : vecr*(hati+hatj+hatk)=5 .

The angle between the lines vecr=(5hati-hatj-4hatk)+lambda(2hati-hatj+hatk) and the plane vecr.(3hati-4hatj-hatk)+5=0 is sin^-1(5/2sqrt91) .

Find the distance of the point (2,12,5) from the point of intersection of the line: vecr=2hati-4hatj+2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr*(hati-2hatj+hatk)=0 .

Find the point of intersection of the line : vecr=(hati+2hatj+3hatk)+lambda(2hati+hatj+2hatk) and the plane vecr*(2hati-6hatj+3hatk)+5=0 .

Find the shortest distance between the lines vecr = (hati + 2hatj+hatk) + lambda(hati-hatj+hatk) and vecr = 2hati - hatj-hatk + mu(2hati+hatj+2hatk)

Find the angle between the lines vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) and vecr=8hati-2hatj+mu(3hati+2hatj+5hatk) .

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the equation of the plane passing through the line (x-1)/2=(y+1)/...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Show that the equation of the plane through the line x/l=y/m=z/n and p...

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  15. Two systems of rectangular axes have the same origin. If a plane cuts ...

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  16. Show that the points P(hati-hatj+3hatk) and Q(3hati+3hatj+3hatk) are e...

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  17. Find in parametric form, the equations of the line x+y+z+1=0, 4x+y-2z+...

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

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

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  20. Find the vector quation of the plane containing the line of intersecti...

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