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Find the shortest distance between the lines `l_1` and `l_2` whose vector equations are `vecgamma=hati+hatj+lambda(2hati-hatj+hatk)` and `vecgamma=2hati+hatj-hatk+mu(3hati-5hatj+2hatk)`

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Find the distance between the lines l_1 and l_2 given by vecr=hati+2hatj-4hatk+lambda(2hati+3hatj+6hatk) and vecr=3hati+3hatj-5hatk+mu(2hati+3hatj+6hatk)

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

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 following pairs of lines : . vecr=3hati+hatj-2hatk+lambda(hati-hatj-2hatk) and vecr=2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

Find the shortest distance between the lines vecr=(-hati+5hatj)+lambda(-hati+hatj+hatk) and vecr=(-hati-3hatj+2hatk)+mu(3hati+2hatj+hatk)

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

Find the shortest distance between the lines vecr=6hati+2hatj+2hatk+lambda(hati-2hatj+2hatk) and vecr=-4hati-hatk+mu(3hati-2hatj-2hatk)

Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-hatj+hatk) and vecr=(2hati+hatj-hatk)+s(2hati-hatj+hatk) .

Find the angle between the pair of lines given by vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) and vecr=5hati-2hatj+mu(3hati+2hatj+6hatk)

NEW JOYTHI PUBLICATION-THREE DIMENSIONAL GEOMETRY-Objective
  1. Find the shortest distance between the lines l1 and l2 whose vector eq...

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  2. The distance between x axis and the point (3,12,5) is

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  3. The perpendicular distance of the point (6,5,8) from y-axis

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  4. If 1/2,1/3,n are the direction cosines of a line , then the value of ...

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  5. A line makes angles of 45^@ and 60^@ with the z-axis and the x-axis re...

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  6. If direction cosines of a line are (1)/(c),(1)/(c),(1)/(c)," then. "

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  7. The coordinates of a point P are (3,12,4) w.r.t. the origin O. Then th...

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  8. The direction cosines of a line that makes equal angles with the three...

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  9. If the direction cosines of a line are k,k,k , then

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  10. The direction cosines of a straight line, whose projections on the coo...

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  11. The vector equation of the straight line (1-x)/3 =(y+1)/(-2) =(3-z)/(-...

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  12. The line (x-x1)/0=(y-y1)/1=(z-z1)/2 is

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  13. A unit vector parallel to the straight line (x-2)/3=(3+y)/(-1) = (z-2)...

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  14. The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d will be perpendicul...

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  15. If the vector equation of a line (x-2)/2=(2y-5)/(-3) =z+1 is vecr=2hat...

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  16. If the staight line (x-1)/k=(y-2)/2=(z-3)/3 and (x-2)/3=(y-3)/k =(z-1)...

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  17. The equation of the line joining the points (-3,4,11) and (1,-2,7) is

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  18. The vector equation of the line 6x-3=3y+4=2z-2 is

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  19. The angle between the staight lines (x+1)/2=(y-2)/5=(z+3)/4 and (x-1)/...

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  20. If the lines (x-1)/(-3)=(y-2)/(2k) =(z-3)/2 and (x-1)/(3k) =(y-5)/1=(z...

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  21. A line makes angles alpha,beta,gamma with the coordinates axes . If al...

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