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If the edges of a rectangular parallelep...

If the edges of a rectangular parallelepiped are a,b, c, prove that the angles between the four diagonals are given by `cos^(-1)"((pma^(2)pmb^(2)pmc^(2))/(a^(2)+b^(2)+c^(2)))`.

A

`cos^(-1)((apm b pm c)/(a+b+c))`

B

`(1)/(2)cos^(-1)((a pm b pm c)/(a+b+c))`

C

`cos^(-1)((a^(2)pm b^(2)pm c^(2))/(a^(2)+b^(2)+c^(2)))`

D

`(1)/(2) cos^(-1) ((a^(2)pm b^(2)pm c^(2))/(a^(2)+b^(2)+c^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
C
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NIKITA PUBLICATION-THREE DIMENSIONAL GEOMETRY -MULTIPLE CHOICE QUESTIONS
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  13. If direction angles of a line are alpha, beta, gamma such that alpha+b...

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