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Find the shortest distance between two lines whose vector equations are : `vecr=3hati+8hatj+3hatk+lambda(3hati-hatj+hatk)` and `vecr=-3hati-7hatj+6hatk+mu(-3hati+2hatj+4hatk)`

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Find the shortest distance between two lines whose vector equations are : vecr=hati+2hatj+hatk+lambda(hati+hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk)

Find the shortest distance between the lines whose vector equations are vecr = (hati+2hatj+3hatk) +lambda(hati-3hatj+2hatk) and vecr = 4hati+5hatj+6hatk+mu(2hati+3hatj+hatk)

Find the shortest distance between the following lines whose vector equations are : vecr=6hati+2hatj+2hatk+lambda(hati-2hatj+2hatk) and vecr=-4hati-hatk+mu(3hati-2hatj-2hatk)

Find the shortest distance between the lines whose equations are : vecr=hati+2hatj+hatk+lambda(hati-2hatj+hatk) and vecr=2hati-hatj-hatk+mu(3hati+hatj+2hatk) .

Find the shortest distance between the following lines whose vector equations are : vecr=(hati-hatj+2hatk)+lambda(-2hati+hatj+3hatk) and vecr=(2hati+3hatj-hatk)+mu(3hati-2hatj+2hatk)

Find the shortest distance between the lines whose equations are : vecr=2hati+3hatj+hatk+lambda(2hati-hatj+3hatk) and vecr=7hati+5hatj+6hatk+mu(hati+3hatj+5hatk)

Find the shortest distance between the following lines whose vector equations are : vecr=(4hati-hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk)

Find the shortest distance between the lines whose equations are : vecr=hati+2hatj+hatk+lambda(hati-hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk) .

Find the shortest distance between the lines whose equations are : vecr=(hati+2hatj+3hatk)+lambda(2hati+3hatj+4hatk) and vecr=(2hati+4hatj+5hatk)+mu(3hati+4hatj+5hatk) .

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Prove that the two lines whose direction cosines are connected by the ...

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  2. Find the general solution of the following (1+secx)dy=y^2dx

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  3. Find the shortest distance between two lines whose vector equations ar...

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

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

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  6. Find the general solution of the following (sinx+cosx)dy=y(cosx-sinx)d...

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

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

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

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

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

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

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

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

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

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

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

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

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

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