|ES-10 Two Dimensional Vectors - Addition|
Vectors possess magnitude and direction.|
Graphically a vector is represented by an arrow, the length of the arrow proportional to the magnitude of the vector and the head of the arrow indicating the direction.
|The vector shown has been resolved into x and y components.|
|If the direction of the vector is indicated with respect to the x axis,|
|From trigonometry we can determine the magnitude of the vector using the Pythagorean Theorem, as well the angle from a major axis.|
|Two or more vectors may be added graphically (Parallelogram Law) or analytically by using components.|
For example, we have two vectors given in terms of magnitude and direction
as shown here.
They may be added graphically by drawing a vector parallel to A
through the head of B and a vector parallel to B through the head of A.
The diagonal connecting the original junction of the tails of A and B and
the opposite corner is the vector sum of A and B.
C represents the vector addition of A and B.
A = 5 cos(25)i + 5 sin(25) j
A = 4.53 i + 2.11 j
B = 4 cos(65) i + 4 sin(65) j
B = 1.69 i + 3.62 j
|1. Resolve both vectors into x and y components where i and j are unit vectors (vectors of magnitude 1) in the x and y directions, respectively.|
C = A + B
C = (4.53+1.69)i + (2.11+3.62)j
C = 6.22 i + 5.73 j
|2. Add like components|
||3. Determine magnitude and direction of C if needed.|