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

• meanyack
In summary, the formula for finding the angle between two vectors C and D is cos(theta) = (C • D) / (|C| * |D|), where theta is the angle between the two vectors and C • D represents the dot product of the vectors. Alpha and beta represent the angle between vector C and the x-axis, and between vector D and the x-axis, respectively. Theta represents the angle between vectors C and D. The dot product of two vectors is found by multiplying each corresponding component of the vectors and then adding the products together. The angle between two vectors is always positive and can be calculated using the aforementioned formula in a 3-dimensional space.
meanyack

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

Attachments

• vectors.JPG
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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?

What is the formula for finding the angle between two vectors?

The formula for finding the angle between two vectors C and D is:
cos(theta) = (C • D) / (|C| * |D|), where theta is the angle between the two vectors and C • D represents the dot product of the vectors.

What are the values of alpha, beta, and theta used for in this calculation?

Alpha and beta represent the angle between vector C and the x-axis, and between vector D and the x-axis, respectively. Theta represents the angle between vectors C and D.

How do I find the dot product of two vectors?

The dot product of two vectors is found by multiplying each corresponding component of the vectors and then adding the products together. For example, if vector C is (c1, c2, c3) and vector D is (d1, d2, d3), the dot product would be: C • D = (c1 * d1) + (c2 * d2) + (c3 * d3).

Can the angle between two vectors be negative?

No, the angle between two vectors is always positive. If the dot product of the two vectors is negative, the angle between them will be greater than 90 degrees.

How do I use this formula to find the angle between vectors in a 3-dimensional space?

In a 3-dimensional space, the formula remains the same, but the dot product will involve three components instead of two. Additionally, the values of alpha, beta, and theta will represent angles in three dimensions instead of just two.

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