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Prove that the angle between any two dia...

Prove that the angle between any two diagonals of a cube is `cos^-1frac{1}{3}`

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MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Show that the line joining the origin to the point (2, 1, 1) is perpen...

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  2. Determine the value of k so that the lie joining the points A(k,1,-1),...

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  3. Prove that the angle between any two diagonals of a cube is cos^-1frac...

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  4. Find the projection of the line segment joining the points: (2,-3,0), ...

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  5. Find the projection of the line segment joining the points (1,2,3), (4...

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

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  7. write the vectoe equation of the line : (x-5)/-3=(y+4)/7=(6-z)/2.

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  8. show that the three lines with direction cosines <12/13,-3/13,-4/13>, ...

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  9. express the following equations of the lines into vector form: (x-3)/3...

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  10. Find the cartesian equation of the line which passes through the point...

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  11. Find the cartesian as well as the vector equation of the line passing ...

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  12. Find the cartesian as well as the vector equation of the line passing ...

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  13. The cartesian equations of a line are : (x-5)/3=(y+4)/7=(z-6)/2 and (x...

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  14. Find the equation of a line parallel to x-axis and passing through the...

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  15. Find the direction cosines of a line parallel to the line :(x-5)/6=(y+...

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  16. Write the direction cosine of a line parallel to the line : (3-x)/3=(y...

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  17. Find the vector and the Cartesian equations of the line through the po...

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  18. Find the equation of the line passing through the point (2, -1, 3) and...

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  19. Find the equation of the line in vector and in cartesian form that pas...

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  20. Find the vector equation for the line through the points : (1,2,2) and...

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