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I have two points A(1, 2) and B(3, 4) and vector AB between them. How can I find the direction of a vector?

I do not know if direction is appropriate word here. By direction I mean following: if I will have point C(2, 1) then I would have to create a vector CD of length, say 2, with the same direction as vector AB and find coordinates of point D.

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1 Answer

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The direction of the vector from point $\;A\;$ to point $\;B\;$ is defined to be

$$\vec{AB}:=B-A=(2,2)$$

Sometimes is useful to take direction vectors of length 1, so you may want to normalize the above:

$$\overline u:=\frac{\vec{AB}}{||\vec{AB}||}=\frac1{2\sqrt2}(2,2)=\left(\,\frac1{\sqrt2},\,\frac1{\sqrt2}\,\right)$$

so you can talk of the direction $\;\vec{AB}\;$ or the direction $\;\overline u\;$ , it just is the same. But read carefully your definitions.

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