11.2 Vectors In Space

This section is about the properties of vectors in 3-D space. The component (regular) form of a vector is
v = <v1,v2,v3>. As we know from earlier chapters, a vector is the difference between a terminal and initial point. Since this is in three dimensions, the three numbers inside the angle brackets are the differences between the x-values, y-values, and z-values, respectively, of a terminal and initial point.


Length of a vector: ||v|| = squareroot(v1^2 + v2^2 + v3^2)

• This equation makes sense, as the length of a vector would be the distance between its initial point and its terminal point. Each vn value is the difference between the x-, y-, or z-value of the terminal and initial points, so this length equation is the same as the basic distance formula we all know and love!