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A line makes angles alpha, beta, gamma, ...

A line makes angles `alpha, beta, gamma, delta` with the diagonals of a cube, prove that `cos^2alpha + cos^2beta + cos^2gamma + cos^2 delta = 4/3`

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the vector equation of the line joining the points A(1,-1,2) and ...

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  2. Find the image of the point (1,6,3) in the line : x/1=(y-1)/2=(z-2)/3.

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

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

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

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

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

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

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

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

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

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

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

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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: vecr=...

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

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

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

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

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