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Prove that the S.D. between a diagonal o...

Prove that the S.D. between a diagonal of a rectangular parallelopiped and its edges not meeting it are: `(bc)/(sqrt(b^2+c^2)),(ca)/(sqrt(c^2+a^2)), (ab)/(sqrt(a^2+b^2))` where a,b,c are lengths of the edges.

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MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. If O be the origin and the coordinates of P be (1, 2, – 3), then find ...

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  2. Find the equation of the plane which contains the line of intersection...

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  3. Prove that the S.D. between a diagonal of a rectangular parallelopiped...

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  4. What is the equation of the xy-plane?

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  5. If a line makes an angle alpha, beta, gamma with x axis, y axis and z ...

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  6. Write the direction cosines of the vector : 2hati+2hatj+3hatk

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  7. Find the vector equation of the line (x+4)/3=(y+3)/7=(z-5)/2

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  8. Find the equation of a st line through (3,1,-5) and equally inclined t...

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  9. The distance of the point (2,3,-5) from the plane x+2y-2z-9=0 is ........

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  10. Find the distance of the plane x-3y+2z-8=0 from the origin.

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  11. Find the intercepts cut off by the plane x+4y-2z=8 with the axes.

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  12. Find the equation of the plane with intercept 9 on the y axis and para...

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  13. What is the point of intersection of the line x=y=z with the plane x+2...

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  14. Distance between the two planes: 2x+3y+4z=4 and 4x+6y+8z = 12 is:

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  15. The planes 2x - y + 4z = 5 and 5x - 2.5y + 10z = 6 are :

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  16. The co-ordinates of foot of the perpendicular drawn from the point (2,...

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  17. If alpha, beta, gamma are the angles that a line makes with the positi...

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  18. The distance of a point P(a,b,c) from x axis is:

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  19. If the direction cosine of a line are < k,k,k >, then,

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  20. The reflection of the point (alpha,beta,gamma) in the xy-plane is:

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