Jump to a New ChapterIntroduction to the SAT IIContent and Format of the SAT II Math IICStrategies for SAT II Math IICMath IIC FundamentalsAlgebraPlane GeometrySolid GeometryCoordinate GeometryTrigonometryFunctionsStatisticsMiscellaneous MathPractice Tests Are Your Best Friends
 8.1 The Coordinate Plane 8.2 Lines and Distance 8.3 Graphing Linear Inequalities 8.4 Other Important Graphs and Equations 8.5 Vectors 8.6 Coordinate Space

 8.7 Polar Coordinates 8.8 Parametric Equations 8.9 Key Formulas 8.10 Review Questions 8.11 Explanations
Vectors
Often used to represent velocity, distance traveled, or force, vectors are line segments defined by two properties: length and direction.
Graphically, a vector is shown as a line segment with an arrow on one end, to show its direction:
In the preceding figure, vector u, which can also be written , has initial point (–2, –2), and terminal point (6, 4). When you see a vector equated to a coordinate pair, say u = (8, 6), like in the figure above, the first coordinate is called the x-component of the vector and the second coordinate is the y-component.
The length of a vector, also known as its magnitude, equals the square root of the sum of the squares of its components. Basically, it’s a restatement of the Pythagorean theorem. The length of the vector above, for example, is = 10.
The length of a vector can be found if you know its initial point and terminal point, or if you know the components of the vector.