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If the edges of a rectangular parallelop...

If the edges of a rectangular parallelopiped are a, b and c, show that the angles between the four diagonals are given by `cos^-1frac{a^2+-b^2+-c^2}{a^2+b^2+c^2}`

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the image of the point (1,6,3) in the line : x/1=(y-1)/2=(z-2)/3.

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  2. A line makes angles alpha, beta, gamma, delta with the diagonals of a ...

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  3. If the edges of a rectangular parallelopiped are a, b and c, show that...

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  4. Find the general solution of the following (1+sinx)dy=ydx

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  5. Prove that the two lines whose direction cosines are connected by the ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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