- Vector: is a quantity that has direction and magnitude
- Scalar: is a quantity that only has magnitude
- True Bearing: is directed compass measurement, beginning at North and rotating clockwise.
- Quadrant Bearing: is a compass measurement east or west of the North-South line
- Equivalent Vectors: are equal in magnitude and direction.
- Vectors can be translated anywhere on the same plane and still be equivalent
- Oppose Vectors: are equal in magnitude, but opposite in direction
- Vectors can be
Adding and Subtracting Vectors
- Since vectors remain equivalent no matter where they are translated, they can be moved around to construct diagrams more convenient for solving.
- Adding Vectors using Tail to head method using a triangle or tail to tail method using a parallelogram.
- The resultant is a vector joining the head of the first vector to the tail of the last vector
- If 2 vectors, a and b, are parallel in the same direction, |a + b| = |a| + |b| and in the same direction
- If a and b have opposite directions and | a | > | b |, then | a + b | = | a | – | b | and a + b is in the same direction as a.
- Subtract vectors by adding the opposite vector
- Zero Vector: means there is no magnitude or direction. Addition of 2 opposite vectors
- Vectors follow commutative, associative, and identity properties
- They can be added in any order
- Simplifying vector expressions is similar to simplifying integer expressions
Scalar Vector Multiplication
- When a vector is multiplied by a scalar, the magnitude is multiplied by the scalar and the vectors are parallel. The directions remains unchanged if the scalar is positive, and becomes opposite if scalar is negative.
- Multiplying vectors follow the distributive and associative rule
- They can be expanded using FOIL
- They can be multiplied in any order
- Linear Combination of vectors can be formed by adding scalar multiples of 2 or more vectors.
Applications of Geometric Vectors
- 2 Vectors that are perpendicular to each other and add together to give a vector v are called the rectangular vector components of v.
- When solving resultants, you can use Vector operations, pythagorean theorem, or trigonometry.
- Equilibriant Vector: is the opposite of the resultant