As shown above, in a 3D-rectangular coordinate system system:
.
Then find the dihedral angle . Submit the angle in degrees and round to the hundredth.
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One of the simplest problems that you post :P
B D = j ^ − i ^ , B E = 2 k ^ − i ^ , B F = 2 j ^ + k ^ .
The required dihedral angle is
cos − 1 ( ∣ B D × B E ∣ ∣ B D × B F ∣ ( B D × B E ) . ( B D × B F ) ) = cos − 1 ( 3 × 6 2 − 2 + 2 ) = cos − 1 ( 3 6 2 ) ≈ 7 4 . 2 0 6 8 3 ° .