Unit vectors

We know that in Physics there are some quantities that need the identification of their intensity (a number followed by a unit of measurement) and their spatial orientation (direction and direction), in order to be well characterized. Such quantities, in Physics, are called vector quantities .

Associating to the x axis a vector , of unit modulus, that presents the same orientation of the axis, the component  can, therefore, be written in the form:

Where Vx is the real number (positive, negative or null) called the projection of the vector  on the x axis. If the component   has the same direction as the x axis, the projection of V x will be a positive number; if it has the opposite direction, V x will be negative. If   it is perpendicular to the x axis, its Vx projection will be zero.

Analogously, associating to the y-axis a vector , with a unit module, with the same orientation as the axis, the component  can thus be written in the form:

Where Vy is the real number (positive, negative or null) called the projection of the vector   on the y-axis. If the component   has the same orientation as the y-axis, the Vy projection will be a positive number; if it has the opposite direction, Vy will be negative. If   it is perpendicular to the y-axis, its Vy projection will be zero.

Resolution

From the figure, we get the following data:

So, the result   is given by:



Since the modules of   and   are equal to 1, we have:




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