Maybe they mean std::vector in C++?

The only correct answer for a 101 introduction. It’s an incredible powerful intuition even in contexts where vectors are seemingly used as a list of numbers.

You can also define a vector by the equivalent “sides of the right triangle”. In 2D, the x,y coordinates. In computer science, vectors are n-tuples, so they represent a math/physics vector but in n-dimensions.

Yes, and as linear algebra teaches, to convert a vector from direction and magnitude to a list of numbers (components), follow these steps:

1. Let the magnitude of the vector be represented by the symbol |A| or A.
2. Let the direction of the vector be represented by the angle θ, which is measured counterclockwise from the positive x-axis.
3. The x-component of the vector is given by: Ax = |A| cos(θ)
4. 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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