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
HereA = 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.