Vectors 1
Vectors provide two pieces of information, magnitude (length or size) and direction (bearing). Vectors are a very graphical form of mathematics which use arrows to represent them. They are probably easiest to see on the Cartesian plane or graph (Cartesian, after the French Mathematician Rene Descartes). Vectors don't have to start at the centre or origin of the graph. Vectors are written with the x component first followed by the y component enclosed between two brackets either horizontally or vertically.
ANWERS:
1) (2,4)
2) (-1,2)
3) (-4,-2)
4) (1,-3)
5) (3,1)
1) (2,4)
2) (-1,2)
3) (-4,-2)
4) (1,-3)
5) (3,1)
Draw arrow diagrams for the following vectors:
ANSWERS:
Vector addition by graphics
To add vectors simply connect them head to tail. For example,
U = (1,2), V = (3,1) Find U + V, see below.
The resulting sum vector (W) can be found by connecting the dots. The new vector (W) is (4,3).
U = (1,2), V = (3,1) Find U + V, see below.
The resulting sum vector (W) can be found by connecting the dots. The new vector (W) is (4,3).
Activity: U = (2,1) and V = (1,2) and W = (3,3) Sketch and hence evaluate
1) U + V
2) U + W
3) V + W
4) U + V + W
Answers:
1) U + V
2) U + W
3) V + W
4) U + V + W
Answers:
Vectors and Trigonometry
There is a strong connection between vectors and trigonometry due to the triangles formed in the process. We can use Pythagoras' Theorem and the trig ratios from SOHCAHTOA. For example find the length of the vector [3,4] above using the Pythagorean theorem. See diagram below.
To calculate the direction or angle use one of the trig ratios