Questions
The lengths of the sides of a rectangular parallelepiped are 11,12,13. Then the angle between two diagonals out of four diagonals is
a
Cos−196232
b
Cos−196434
c
Cos−196217
d
Cos−11924434
detailed solution
Correct option is C
If OA¯,OB¯ , OC¯are considered as coordinate axes respectively such that OA=13,OB=12,OC=11, Direction ratios of two diagonals AF¯,BE¯are 13,−12,−11 and 13,−12,11respectively.If θbe the angle between the above two diagonals thencosθ=a1a2+b1b2+c1c2a12+b12+c12a22+b22+c22=169+144−121169+144+1212=192434=96217Therefore, θ=arccos96217Talk to our academic expert!
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Angle between the lines whose direction ratios are a,b,c and is
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