7.1. Basic Properties of Vectors http://www.ck12.org
One way to define a vector is as a line segment with a direction. Vectors are said to be equal if they have thesame
magnitudeand thesame direction. Theabsolute value of a vectoris the same as thelength of the line segmentor
themagnitude of the vector. Magnitude can be found by using the Pythagorean Theorem or the distance formula.
There are a few different ways to write a vectorv.
v,−→v,⇀v,orvwith a∼ underneathWhen you write about vectors algebraically there are a few ways to describe a specific vector. First, you could
describe its angle and magnitude asr,θ. Second, you could describe it as an ordered pair:<x,y>. Notice that
when discussing vectors you should use the brackets<>instead of parentheses because it helps avoid confusion
between a vector and a point. Vectors can be multidimensional.
Example A
A ship is traveling NNW at 17 knots (nautical mph). Describe this ship’s movement in a vector.
Solution: NNW is halfway between NW and N. When describing ships at sea, it is best to use bearing which has
0 ◦as due North and 270◦as due West. This makes NW equal to 315◦and NNW equal to 337. 5 ◦.