**Vectors**

**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