VECTORS

  1. Vectors have a size, or magnitude, and a direction. They are usually represented by an arrow with a length scaled to the magnitude and the arrow pointing in the direction.
    1. Scalars have only magnitude.
    2. Examples of vectors are: displacement, velocity, and acceleration
    3. Examples of scalars are mass and speed.
  1. Vectors can be added using a graphical method.
  2. Vectors can be added using components.

A. A unit vector is a vector that is 1 unit long and points in the specified direction.

B. The unit vectors: i - points along the x-axis in the positive x-direction; j - points along the y-axis in the positive y-direction; k - points along the z-axis in the positive z-direction.

C. For the vector A

 

Here A = Axi + Ayj

Ax = Acosq and Ay = Asinq

Note that A2 = Ax2 + Ay2 and that tanq = Ay/ Ax

D. If we have a second vector B that makes an angle of b with the x-axis, then we can write that the vector C is the vector sum of A and B.

C = A + B

Cxi + Cyj = (Axi + Ayj) + (Bxi + Byj)

 

Cxi + Cyj = (Ax + Bx)i + (Ay+ By)j

Cx = (Ax + Bx) = Acosq + Bcosb

Cy = (Ay + By) = Asinq + Bsinb

III. Vectors can also be multiplied, but this will be introduced later in the course.