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Find the shortest distance between each of the following pair of lines:
`vecr=(8+3t)hati-(9+16t)hatj+(10+7t)hatk` and `vecr=15hati+29hatj+5hatk+s(3hati+8hatj-5hatk)`.

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Find the shortest distance between each of the following pair of lines: vecr=(4hati-5hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk) .

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Find the shortest distance between the lines vecr= (8+3lambda) hati-(9+16 lambda)hatj+ (10+7 lambda)hatk" and "vecr = 15hati+29hatj+5hatk + mu(3hati+8hatj-5hatk) .

Find the angles between each of the following pairs of lines: vecr=4hati-hatj+lambda(hati+2hatj-hatk) and vecr=hati-hatj+2hatk-mu(2hati+4hatj-4hatk)

Find the shortest distance between the following lines whose vector equations are : vecr=(8+3lambda)hati-(9+16lambda)hatj+(10+7lambda)hatk and vecr=15hati+29hatj+5hatk+mu(3hati+8hatj-5hatk)

Find the shortest distance and the equation of the shortest distance between the following two lines: vecr=(-hati+hatj+9hatk)+lambda(2hati+hatj-3hatk) and vecr=(3hati-15hatj+9hatk)+mu(2hati-7hatj+5hatk)

Find the angle between the following pair 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 whose equations are : vecr=(hati-hatj+2hatk)+lambda(2hati-hatj+4hatk) and vecr=(2hati-4hatj+hatk)+mu(3hati+hatj-5hatk) .

Find the shortest distance between the following lines whose vector equations are : vecr=(3-t)hati+(4+2t)hatj+(t-2)hatk and vecr=(1+s)hati+(3s-7)hatj+(2s-2)hatk where t and s are scalars.

Find the angle between the following pair of lines : vecr=hati+hatj-hatk+lambda(hati-3hatj+2hatk), vecr=2hati-hatj+hatk+mu(3hati+hatj-2hatk)

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
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  2. Find the general solution of the following (sinx+cosx)dy=y(cosx-sinx)d...

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  3. Find the shortest distance between each of the following pair of lines...

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  4. Find shortest distance between lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-2)...

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  5. Determine whether or not the following paris of lines intersect: vecr=...

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  6. Determine whether or not the following paris of lines intersect: vecr=...

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  7. Determine whether or not the following paris of lines intersect: (x-1)...

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  8. Find the general solution of the following (1+x^2)dy=xydx

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  9. Find the general solution of the following (e^x+1)dy=y(e^x)dx

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  10. Show that the lines (x-1)/23=(y+1)/2=(z-1)/5 and (x-2)/4=(y-1)/3=(z+1)...

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  11. Write the vector equation of the following lines and hence find distan...

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  12. Find the normal unit vector to the plane x+2y+3z-6=0.

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  13. Find the unit vector perpendicular to the plane vecr.(6hati+3hatj-2hat...

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  14. Find the cartesian equation of the following planes: vecr.(hati+hatj+h...

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  15. Find the cartesian equation of the following planes: vecr.(2hati-3hatj...

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  16. Find the equations of the line passing through the point (1,-1,2) and...

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  17. Find the equation of the line passing through the point with position ...

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  18. Find the general solution of the following (1+logx)xdy=ydx

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  19. Find the equation of the plane passing through the point (3,-3, 1) and...

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  20. Find the equation of a plane which bisects perpendicularly the line se...

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