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

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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 shortest distance between the lines whose vector equations are vecr = (1-t)hati + (t-2)hatj + (3-2t)hatk and vecr = (s+1)hati + (2s-1)hatj - (2s+1)hatk

Find the shortest distance between the following lines whose vector equations are : vecr=(lambda-1)hati+(lambda-1)hatj-(1+lambda)hatk and vecr=(1-mu)hati+(2mu-1)hatj+(mu+2)hatk

Find the shortest distance between the following lines whose vector equations are : vecr=(1+lambda)hati+(2-lambda)hatj+(1+lambda)hatk and vecr=2(1+mu)hati-(1-mu)hatj+(-1+2mu)hatk

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 following lines whose vector equations are : vecr=3hati-15hatj+9hatk+lambda(2hati-7hatj+5hatk) and vecr=(2mu-1)hati+(1+mu)hatj+(9-3mu)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 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 following lines whose vector equations are : vecr=(hati+2hatj-4hatk)+lambda(2hati+3hatj+6hatk) and vecr=(3hati+3hatj-5hatk)+mu(2hati+3hatj+6hatk)

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)

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Change to normal form the plane 2x-3y+6z+4=0

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  2. Find the vector equation of the following planes in scalar product for...

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  3. Find the shortest distance between the following lines whose vector eq...

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  4. Find the vector equation of the following plane in scalar product form...

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  5. Find the equation satisfied by the coordinates of a variable point P(x...

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  6. Find the vector equations of the plane passing through the points R(2...

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  7. Prove that the normal to the plane containing three point whose positi...

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  8. Find the equation of a plane which is at a distance 3sqrt3 units from ...

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  9. Show that the plane whose vector equation is vecr.(hati+2hatj-hatk)=3 ...

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  10. Find the equation of the plane through the points (2,2,-1) and (3,4,2)...

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  11. Find the equation of the plane which passes through the line (x-3)/2=(...

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  12. Find the equation of the plane containing the line (x-3)/7=(y-4)/0=(z-...

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  13. Find the equation of the plane containing the line (x+1)/-3=(y-3)/2=(z...

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

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  15. Find the equation of the plane which is parallel to the line (x-4)/1=(...

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  16. Find the equation of the plane parallel to the line (x-2)/1=(y-1)/3=(z...

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  17. Evaluate int dx/(secx + tanx)

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  18. Find the equation of the line passing through (1,2,3) and parallel to ...

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  19. Find the equation of the plane, which contains two lines: (x-4)/1=(y-3...

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  20. Find the equation of the plane containingg the lines: vecr=hati+hatj+l...

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