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State when the line vecr=veca+lambdavecb...

State when the line `vecr=veca+lambdavecb` is parallel to the plane `vecr*vecn=d`. Show that the line `vecr=hati+hatj+lambda (2hati+hatk+4hatk)` is parallel to the plane `vecr*(-2hati+hatk)=5`. Also, find the distance between the line and the plane.

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Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr*(hati+2hatj-hatk)=3 .

Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) lies in the plane vecr*(3hati+hatj-hatk)+2=0 .

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

Show that the line L whose vector equation is vecr=2hati-2hatj+3hatk+lambda(hati-hatj+4hatk) is parallel to the plane pi whose vector equation is vecr*(hati+5hatj+hatk)=5 and find the distance between them.

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

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Find the equation of the plane containing the line : (x-1)/3=(y+2)/1=(...

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

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  3. State when the line vecr=veca+lambdavecb is parallel to the plane vecr...

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  4. Find the equations of the line through (-1,3,2) and perpendicular to t...

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  5. Find the vector equation of the line passing through the point (3,1,2)...

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  6. Find the vector equation of a line passing through the point with posi...

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

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  8. Find the length of the perpendicular from the point (1,2,3) to the lin...

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  9. Find the point, where the line joining the points (1,3,4) and (-3,5,2)...

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  10. Find the co-ordinates of the point where the line joining the points (...

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  11. Find the equation of the plane passing through the point (1,1,1) and c...

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

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  13. Find the vector equation of the plane passing through three points wit...

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  14. A line makes 90^@, 135^@, 45^@ with x, y and z axes respectively than ...

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  15. Find the direction cosine of a line which makes equal angles with the ...

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  16. If a line has the direction ratios –18, 12, – 4, then what are its dir...

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  17. Show that the points (2, 3, 4), (– 1, – 2, 1), (5, 8, 7) are collinear...

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  18. Find the direction cosines of the sides of the triangle whose vertices...

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  19. show that the three lines with direction cosines <12/13,-3/13,-4/13>, ...

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  20. Show that the line through the points (1, – 1, 2), (3, 4, – 2) is perp...

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