Cuboids

Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)

Result

a =  62.78 °

Solution:

s=0.62955056⋅ 0.14484653+0.094432584⋅ 0.9208101+0.77119944⋅ 0.36211633≐0.4574 a=180∘π⋅arccos⁡(s)=180∘π⋅arccos⁡(0.4574)≐62.7801≐62.78∘≐62∘46′48"s=0.62955056 \cdot \ 0.14484653 + 0.094432584 \cdot \ 0.9208101 + 0.77119944 \cdot \ 0.36211633 \doteq 0.4574 \ \\ a=\dfrac{ 180^\circ }{ \pi } \cdot \arccos( s )=\dfrac{ 180^\circ }{ \pi } \cdot \arccos( 0.4574 ) \doteq 62.7801 \doteq 62.78 ^\circ \doteq 62^\circ 46'48"

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Matikar
use scalar products to determine angle between two 3D vectors (if direction cosines gives -> its unit vectors)

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