The ∑ symbol asks you to evaluate the function 2 + 3n for all of the values of n from 0 through 4
inclusive and then sum their values.
VECTORS
Some properties, such as force, velocity, or acceleration, need more than just a number to describe
them. We must know direction as well as size or magnitude in order to work with them. Those
quantities that are described by both direction and magnitude are called vectors. Since vectors have
information about both magnitude and direction, we draw them with arrows.
Two vectors are equal if and only if they are equal in both magnitude and direction. So is not equal
to , although they are the same length, because they are in different directions.
In plane geometry, two lines are perpendicular if their slopes are negative reciprocals of each other.
In vector geometry, two vectors are perpendicular if and only if their dot product
is zero.
If is a vector, then is defined as having the same magnitude but the reverse direction to .
Subtracting is the same as adding .
Multiplying a vector by a number just has the effect of changing its scale. So, for example, would
be twice as long as and also in the same direction as .
When two vectors are continuous (like a traveling vehicle that makes a turn), you can use the
triangle law of addition and treat the two vectors as though they were sides of a triangle.