The magnitude of vector x is written as |x|.
The magnitude of vector is written as |AB|.
A vector with magnitude 0 is called the zero vector, written 0. A vector with magnitude 1 is called a unit vector.
Vectors are equal if they have the same magnitude and the same direction.
a = b
The inverse of a vector is a vector of equal magnitude but in the opposite direction. The inverse of is - or and the inverse of a is -a.
Scalars have magnitude but not direction. Vectors can be multiplied by a scalar to produce another vector.
Multiplying vector x by 3 will give a new vector 3 times the length and parallel to x.
When 2 vectors are added or subtracted the vector produced is called the resultant.
The resultant is identified by a double arrowhead.
To add two vectors you apply the first vector and then the second.
a + b = c
Subtracting a vector is the same as adding its inverse.
a – b is the same as a + (-b)
Moving from A to C through B is the same as moving through D.
+ = + =
a + b = b + a = c