I. Key Terms and Phrases
vector a mathematical quantity having both
magnitude and direction (with appropriate units)
scalar a numerical value with appropriate units
magnitude of a vector the full numerical value of the quantity being represented
direction of a vector the orientation within a coordinate system of the quantity being represented
component of a vector the part of a vector associated with a specific direction
unit vector a dimensionless of unit magnitude
II. Important Equations
| Name/Topic | Equation | Explanation |
| scalar components of a vector V |
 |
Scalar components of a vector from its magnitude and direction. The angle q is measured from the +x direction. |
| reference angle |
 |
The reference angle gives the direction of a vector with respect to the coordinate axes. |
| magnitude of a vector |
 |
The magnitude of a vector from its x- and y-components. |
| unit vectors |
 |
A two-dimensional vector written in terms of unit vectors. |
| vector addition/subtraction |
 |
Vector addition and subtraction with components. |
| relative motion |
vPA = vPB + vBA |
Velocity addition for relative motion using the subscripting mnemonic. |
III. Know Your Units
| Quantity | Dimension | SI Unit |
| unit vector |
-- |
dimensionless |
IV. Tips
The component method of vector addition described in this chapter is very powerful
and always works. However, the method can sometimes be cumbersome, and increasing
the number of calculations provides greater opportunities for some sort of
mistake to slip in. For cases when you know the magnitudes and direction
of the two vectors you need to add, the law of cosines can provide a more
direct route to the result than the component method. The law of cosines
is illustrated below.
Consider the many calculations in the solution of Example 3-4. If we only needed the magnitude of v3, having been given the magnitude and direction of both v1 and v2 would have allowed us to immediately write down the following triangle:
The law of cosines would then yield the result with just one additional step
V. Additional Tools
Recording
Calculator
This is a 'printing' scientific calculator. It allows you to check your calculations
by reviewing your work.
Scientific
Calculator
This is a standard scientific calculator.
Graphing
Calculator
This is a simple graphing calculator, the JavaScript resource of the month
for several months at Developer.com.
Physical
Constants
This is a searchable database of physical constants.
Conversion
Engine
This conversion factor tool gets almost 1000 hits a day and has been featured
by Microsoft.
