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Determine whether or not the following p...

Determine whether or not the following pairs of lines intersect : `vecr=(2lambda+1)hati-(lambda+1)hatj+(lambda+1)hatk` and `vecr=(3mu+2)hati-(5mu+5)hatj+(2mu-1)hatk `

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Determine whether or not the following pairs of lines intersect : vecr=(hati-2hatj+3hatk)+lambda(-hati+hatj-2hatk) and vecr=(hati-hatj-hatk)+mu(hati+2hatj-2hatk)

Determine whether or not the following paris of lines intersect: vecr=hati-5hatj+lambda(2hati+hatk) , vecr=2hati-hatj+mu(hati+hatj-hatk) .

Determine whether or not the following paris of lines intersect: vecr=hati-hatj+lambda(2hati+hatk) , vecr=2hati-hatj+mu(hati-hatj-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=(lambda-1)hati+(lambda-1)hatj-(1+lambda)hatk and vecr=(1-mu)hati+(2mu-1)hatj+(mu+2)hatk

Determine whether the following pair of lines intersect : vecr=hati+hatj-hatk+lamda(3hati-hatj) and vecr=4hati-hatk+mu(2hati+3hatk)

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 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 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 vecr= (8+3lambda) hati-(9+16 lambda)hatj+ (10+7 lambda)hatk" and "vecr = 15hati+29hatj+5hatk + mu(3hati+8hatj-5hatk) .

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Find the S.D. between the lines : (x-3)/3=(y-8)/-1=(z-3)/1 and (x+3)/-...

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  2. Determine whether or not the following pairs of lines intersect : vecr...

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  3. Determine whether or not the following pairs of lines intersect : vecr...

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  4. Determine whether or not the following pairs of lines intersect : (x-1...

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  5. Prove that the lines : (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-2)/(3)=(y-...

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  6. Find the shortest distance and the equation of the shortest distance b...

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  7. Find the shortest distance and the vector equation of the line of shor...

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  8. How many cubic feet are there in a room measuring 5m x 10m x 2m?

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

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  10. Show that the lines : (x+1)/3=(y+3)/5=(z+5)/7 and (x-2)/1=(y-4)/3=(z-6...

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  11. Show that the lines : vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) ...

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  12. Show that the lines: vecr=(hati+hatj-hatk)+lambda(3hati-hatj) and vecr...

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

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  14. Show that the lines: vecr=(hati+hatj)+lambda(2hati-hatk) and vecr=(2ha...

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

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  16. Show that the following lines are coplanar (5-x)/-4=(y-7)/-4=(z+3)/-5 ...

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

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  18. Show that the lines (x-a+d)/(alpha-delta) = (y-a)/alpha = (z-a-d)/(alp...

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  19. Find the equations the lines joining the following pair of vertices : ...

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  20. Find the equations the lines joining the following pair of vertices: (...

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