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# Vectors: direction vector - slope proof watch

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1. write down the slope of the line in the direction of the vector

which is
=

=

and the general form
write down the slope of the line in the direction of the vector

which is
=

^^ can someone show me the proof for this
2. By the looks of it it's just a definition; but intuitively, you generalise from the 2D case.

The slope is how far you travelled 'up' divided by how much you travelled 'across'. In the 2D case this simply means , but in the 3D case, 'up' is now the z-direction, and 'across' is how far along the (x,y)-plane you travelled. Hence, .

More generally, i.e. if you start from a point rather than from the origin, this definition would give .
3. (Original post by nuodai)
By the looks of it it's just a definition; but intuitively, you generalise from the 2D case.

The slope is how far you travelled 'up' divided by how much you travelled 'across'. In the 2D case this simply means , but in the 3D case, 'up' is now the z-direction, and 'across' is how far along the (x,y)-plane you travelled. Hence, .

More generally, i.e. if you start from a point rather than from the origin, this definition would give .
thank you!
just needed someone to point out that bit of intuition...
too much stats in the past week has ruined me

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