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)

Correct result:

a =  62.7801 °

Solution:

$$\begin{gathered} s=0.62955056\cdot 0.14484653+0.094432584\cdot 0.9208101+0.77119944\cdot 0.36211633\doteq 0.4574 \\ a={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arccos (s)={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arccos (0.4574)=62.7801^{\circ }=62^{\circ }46^{\mathrm{\prime }}48\mathrm{"} \end{gathered}$$

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Matikar

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

3 years ago  Like

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