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Vectors and mechanics

How does rxc=d give you the equation of a line with direction vector c? Surely it gives you a line perpendicular to both the direction vector and any point on the line?

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Assuming "x" is * and r is a constant (not a vector), you are simply scaling the vector c. If r is not 1 all you are doing is changing the magnitude of the vector.
2 * [1,3,6] = [2,6,12] (3d vector, with x,y and z)
Note how the third element is still twice as the second, which is three times as big the first.

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