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Vectors in a plane

Unit vector
A vector and the associated unit vector. The unit vector always has the magnitude of 1 and the same direction as the original vector.

Position vector

A position vector is a vector representing the position of a point in relation to a fixed point, for instance (0,0).

Unit vector

A unit vector (sometimes called normalized vector) has the magnitude of 1.
It is possible to convert a vector to a unit vector by dividing its coordinates with its magnitude:

 ->{u}=frac{ ->{a}}{| ->{a}|}=(frac{a_x}{| ->{a}|},frac{a_y}{| ->{a}|})

Calculate the unit vector

Please enter the x- and the y-coordinate of the vector.