Graphing a vector with component angles?

In summary, the conversation discussed how to graph a resultant vector with given magnitude and angles in component form. The method involved using dot product with unit vectors to calculate the components of the vector in the x, y, and z directions.
  • #1
Psych Berry
15
0
At the end of a problem (I'm sure I did all the math correctly, that's not an issue) I'm supposed to graph the corresponding resultant vector. However, along with the magnitude of the vector, the angles given are in component form: θx, θy, θz. I've never encountered this before, and although it seems like it's probably easy, I have no idea how to graph such a vector. Can anyone explain how, or is there anything anyone knows of that I can use a reference?
 
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  • #2
Say your vector is R, with components as such <Rx,Ry,Rz>. To get the angle R makes with the x-axis, you'd dot product R with <1,0,0> (unit vector in direction of the x-axis).

This gives
<Rx,Ry,Rz>.<1,0,0>=|R|(1)cosθx

Or simply Rx=|R|cosθx

Do a similar exercise with the unit vectors in the direction of the y and z axes to get the components Ry and Rz
 

1. What is a vector with component angles?

A vector with component angles is a way of representing a vector in two-dimensional space by breaking it down into two components, one in the horizontal direction (x-axis) and one in the vertical direction (y-axis).

2. How do I graph a vector with component angles?

To graph a vector with component angles, start by drawing a coordinate system with the x-axis and y-axis labeled. Then, use the component angles to determine the direction of the vector. The x-component will be the length of the vector in the horizontal direction, and the y-component will be the length of the vector in the vertical direction.

3. What is the magnitude of a vector with component angles?

The magnitude of a vector with component angles can be found using the Pythagorean theorem. It is equal to the square root of the sum of the squares of the x-component and y-component of the vector.

4. Can a vector with component angles have negative components?

Yes, a vector with component angles can have negative components. This means that the vector will point in the opposite direction of the positive component. For example, if the x-component is negative, the vector will point to the left instead of the right.

5. How can I find the angle of a vector with component angles?

The angle of a vector with component angles can be found using trigonometric functions. The tangent of the angle is equal to the y-component divided by the x-component. Use a calculator or table of trigonometric values to find the angle.

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