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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)`

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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) .

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by : vecr= (-4hati+4hatj+hatk)+lambda(hati+hatj-hatk) and vecr=(-3hati-8hatj-3hatk)+mu(2hati+3hatj+3hatk) .

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 each of the following pair of lines: vecr=3hati+5hatj+7hatk+lambda(hati-2hatj+7hatk) and vecr=-hati-hatj-hatk+mu(7hati-6hatj+hatk) .

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by : vecr= (3hati+8hatj+3hatk)+lambda(3hati-hatj+hatk) and vecr=(-3hati-7hatj+6hatk)+mu(-3hati+2hatj+4hatk) .

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 lines whose equations are : vecr=5hati+3hatj+2hatk+lambda(2hati+hatj-hatk) and vecr=3hati-hatj-2hatk+mu(hati+hatj+2hatk)

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

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 lines whose equations are : vecr=hati+2hatj+hatk+lambda(hati-hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk) .

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Determine whether or not the following pairs of lines intersect : (x-1...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Find the shortest distance between the lines ((x+1)/7=(y+1)/-6=(z+1)/1...

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

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  20. Find the equation of the plane with the intercept 5 on the y axis and ...

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