Components of a vector

One way we can find the components of a vector is by putting the tail or initial point of a vector at the origin of a coordinate system.

A vector

We find the components by drawing perpendicular lines from the head or terminal point to the axis. The vectors shown in red are the components of vector A.

Components of a vector
Ax and Ay are the components of vector A.

Equations for the components of a vector

Some simple trigonometry can help us find some equations for the components and the angle t.

cos(t) =
Ax / A

Ax = A cos(t)

sin(t) =
Ay / A

Ay = A sin(t)

The components of a vector are given by

Ax = A cos(t)
Ay = A sin(t)

To find the magnitude of A, we can use the pythagorean theorem.

A = √((Ax)2 + (Ay)2)

To find the angle, use tan(t) =
Ay / Ax

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