? = (shift) / (phenomenon)
(shift) (properties) () (magnitude), () (direction).
,
() , ()
0 1 2 3 4 5 6 7 8 9 --+---+---+---+---+---+---+---+---+---+--
o------------------>o----------> 5 3
o------------------------------> 8
, , ,
, , , - , , , , , , , , Draw an arrow on a piece of paper,
pointing in any direction, and you have a vector: a length with a
direction. Draw another arrow starting at the tip of the first one,
and you have added two vectors:Draw an arrow on a piece of paper,
pointing in any direction, and you have a vector: a length with a
direction. Draw another arrow starting at the tip of the first one,
and you have added two vectors:
--+ /|\ u+v/ \v / \ / \ o--------->o u
If you draw vectors on a coordinate grid, you can give them
names:
V(-2,3) ^ W(3,3) + | + \ | / \ v\ |u+v/ \v \ | / \ \| / \
o---------->o------> u U(5,0)
Place each vector so that it starts at the origin (0,0), and
name it for the point where it ends, just as we did on the number
line. Our vectors are u = (5,0) and v = (-2,3), since they end at
points U and V as shown. Their sum w = u+v is (3,3). Do you see how
to add two vectors? You just add their x coordinates and their y
coordinates; u goes 5 to the right and v goes 2 to the left, so w
goes 5-2 = 3 to the right. (Actually, we use the word "coordinate"
only for points; for vectors, we use the word "component.")
You can do the same for vectors in three-dimensional space, but
I won't bother drawing that. The important thing is that vectors
give us a way to talk about anything that has both size and
direction, but not position - things like velocities, wind speeds,
forces, and so on. If I row my boat in the direction of vector u,
but the water itself is moving along vector v, then I will actually
be moving along vector u+v, so the sum of the two vector velocities
tells me how fast, and in what direction, I am really going.
For an introduction to vectors with nicer pictures, try
this:
Vectors - Gene Klotz, The Math Forum
http://mathforum.org/~klotz/Vectors/vectors.html
Here's another; look under "Basic Stuff":
Maths Help - Working with vectors - Jenny Olive
http://www.netcomuk.co.uk/~jenolive/homevec.html
If you have any further questions, feel free to write back.
- Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Associated Topics:High School Linear Algebra
Search the Dr. Math Library:
Find items containing (put spaces between keywords): Click only
once for faster results: [ Choose "whole words" when searching for
a word like age.]
all keywords, in any order at least one, that exact phrase parts
of words whole wordsSubmit your own question to Dr. Math[Privacy
Policy] [Terms of Use]
_____________________________________Math Forum Home || Math
Library || Quick Reference || Math Forum Search
_____________________________________Ask Dr. MathTM 1994-2015 The
Math Forumhttp://mathforum.org/dr.math/
How to find the Vector Equation of a Line segment?
