Noncollinear vectors are vectors that exist in more than one dimension (i.e. they are located along different straight lines).
These vectors cannot be added algebraically; however, they can be added graphically using the tail to tip method described in the previous lesson.
Sample Problem 1
Sheila left the school at noon to go jogging. She ran 3 km [S], 5 km [E], 2 km [S] and finally 4 km [W]. Determine the resultant vector.
Graphical methods are useful to conceptualize a situation but because of its inherent errors it is really only useful as a first approximation for mathematical methods.
If vectors form a right angle triangle (i.e. they are perpendicular vectors),
Pythagorean theorem
and
a trigonometric ratio
can be used to determine the resultant vector.
Angle Explanation:
will be the angle from the resultant vector to the nearest xaxis. You can determine what quadrant the angle will be in by looking at the sign of and :
If is +
If is +
The angle will be in quadrant I.


If is +
If is 
The angle will be in quadrant II.


If is 
If is +
The angle will be in quadrant III.


If is 
If is 
The angle will be in quadrant IV.



Sample Problem 2
A sailboat sails 230 km [E] and then 340 km [N]. Determine its resultant vector.
Solution
Since these vectors are perpendicular you can use the Pythagorean theorem to determine the length of the resultant vector and a trigonometric ratio to determine the angle involved.
The magnitude of the resultant vector is 410 km.
Since and are positive the angle will be in quadrant I.
The angle from the positive xaxis is 55.9° . Therefore using our convention for direction the angle would be expressed as [N 34.1° E].
The resultant vector would be 410 km [N 34.1° E].
Sample Problem 3
A football player is hoping to score a touchdown by running a complicated play. He runs 5 m [N 36° E], then changes his path to run 12 m [N 52° W] where he meets a block and is forced to run 15 m [S 73° E] before he is tackled. Determine the resultant vector. Did this player have a successful play?
