Unit Vectors

Instead of explicitly writing A_x = 5, A_y = 0; B_x = 5, B_y = 5; C_x = - 10, C_y = 0; and D_x = - 5, D_y = 5, we can write this same information in a different form. We can write

A = 5 i + 0 j

B = 5 i + 5 j

C = - 10 i + 0 j

D = - 5 i + 5 j

i and j are "unit vectors" in the x- and y-directions. Being "unit vectors", they each have a magnitude of one. They carry only the direction information.

Now we can write

R = A + B + C + D

R = (5 i + 0 j) + (5 i + 5 j) + (- 10 i + 0 j) + (- 5 i + 5 j)

R = ( 5 + 5 - 10 - 5 ) i + ( 0 + 5 + 0 + 5 ) j

R = - 5 i + 10 j

Now we know the components of the resultant,

R_x = - 5

and

R_y = 10

and we can proceed exactly as before to recombine those to find the magnitude and the direction.

To explicitly remind ourselves that i and j are "unit vectors", they are sometimes (or oftentimes) written with a "hat" or "caret" above them,

Vector Components			Displacement, Velocity, and Acceleration
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(c) 2005, Doug Davis; all rights reserved