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Find shortest distance between lines `(x-1)/2=(y-2)/3=(z-3)/4` and `(x-2)/3=(y-4)/4=(z-5)/5`

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MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. 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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  2. Show that the lines: vecr=(hati+hatj)+lambda(2hati-hatk) and vecr=(2ha...

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

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

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

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

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

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

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

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

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  12. Find the equation of the plane with intercept 4 on the z axis and para...

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  13. Find the vector equation of a plane, which is at a distance of 7 uits ...

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  14. Find the vector equation of a plane, which is at a distance of 5 units...

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  15. Find the vector equation of the plane whose cartesian form of equation...

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  16. Find the vector equation of the plane whose cartesian form of equation...

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  17. Find the cartesian equations of the following planes: vecr*(3hati+3hat...

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  18. Find the cartesian equations of the following planes: vecr*(2hati+3hat...

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  19. Find the Cartesian equation of the following plane: vecr cdot [(s-2t)h...

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  20. What are the direction cosines of the normal to the plane 3x+2y-3z=8?

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