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.

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.

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

Enter Your E-mail Address
Enter Your First Name (optional)

Don't worry — your e-mail address is totally secure.
I promise to use it only to send you Physics lessons.

New! Comments

Do you like the physics lessons on this site? Have your say about what you just read! Leave me a comment in the box below. Please share the lessons with your friends as well!