3d vectors & ejection seats
I am doing research on ejection seats. Any good references on 3D
vectors for HS students without a calculus background?
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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Update: June 2012