Yes, and as linear algebra teaches, to convert a vector from direction and magnitude to a list of numbers (components), follow these steps:
- Let the magnitude of the vector be represented by the symbol |A| or A.
- Let the direction of the vector be represented by the angle θ, which is measured counterclockwise from the positive x-axis.
- The x-component of the vector is given by: Ax = |A| cos(θ)
- The y-component of the vector is given by: Ay = |A| sin(θ)
The vector can now be represented as a list of numbers: A = (Ax, Ay)
For example, if a vector has a magnitude of 5 units and a direction of 30° counterclockwise from the positive x-axis, its components would be:
Ax = 5 cos(30°) ≈ 4.33 units Ay = 5 sin(30°) ≈ 2.50 units
The vector can now be written as A = (4.33, 2.50)
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