Find Angle Between Vectors C & D Using Alpha, Beta & Theta

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To find the angle between vectors C and D using angles α, β, and θ, the discussion emphasizes the use of the cross product and dot product formulas. The cross product formula, u X v = |u||v|sin(angle), can be rearranged to solve for the angle, but complications arise when considering the angle between vector C and the plane formed by vectors A and B. Participants express concerns about the complexity of this calculation and seek simpler methods to determine the angle. The conversation highlights the need for clarity in vector relationships and the potential challenges in applying standard formulas in this context. Overall, the thread seeks an efficient approach to calculate the angle between the specified vectors.
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Homework Statement



Please find the attachment for vectors. If I know \alpha, \beta & \theta (colored angles) how can I find the angle between vectors C and D in terms of \alpha, \beta & \theta?

Homework Equations



Cross product & dot product

The Attempt at a Solution

 

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The cross product is defined by u X v = |u||v|sin(angle). Solve for the angle.
 
At first glance, it seems easy. But when you try to find the angle between vector C and plane consisting A and B, then it seems complicated. So is there any way to calculate it easily?
 

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