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Question:
I am doing research on ejection seats. Any good references on 3D vectors for HS students without a calculus background?



Replies:
Well, you do not need to know anything about calculus to understand vectors. A vector can be thought of in a number of different ways, but the most general for physics purposes is a combination of two different things - a vector gives (1) a direction, and (2) a magnitude (ie. length). The concept of direction is pretty simple - just follow along the way the vector is pointing, and it is the same concept whether you are in 2 dimensions, 3D, or even any arbitrary number of dimensions (higher dimensions turn up all the time in mathematics, though they may or may not have much to do with the real world). The magnitude tells you something about the size of whatever property is associated with that direction - it could be a force, or a velocity, or an acceleration, or just a particular change in position. Of course, a vector is usually represented as a collection of numbers that indicate its components along standard directions (usually the x, y, z axes in 3D). And then the magnitude is the square root of the some of the squares of the components (sorrow, that should be "sum") ie. magnitude = sqrt(vx^2 + vy^2 + vz^2) where the vector is represented as (vx,vy,vz). Hope that helps



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