This document discusses key concepts related to vector quantities in physics: 1. A vector is represented by an arrow that shows both magnitude and direction, such as the velocity of an object. 2. Vector addition and subtraction can be done graphically by drawing vectors head-to-tail to find the resultant vector. 3. The Pythagorean theorem can be used to add perpendicular vectors numerically by treating them as components of the overall resultant vector.

1. Vectors Notes

2. VELOCITY VECTORS VECTOR: An arrow drawn to scale that represents the magnitude and direction of a given velocity. 10m/s left 5m/s rt

3. Scaled Vector Diagrams There are several characteristics of this diagram which make it an appropriately drawn vector diagram. a scale is clearly listed a vector arrow (with arrowhead) is drawn in a specified direction. The vector arrow has a head and a tail . the magnitude and direction of the vector is clearly labeled.

4. Direction Conventions Use East as zero degrees. Click here to practice: Practice set at The Physics Classroom

5. RESULTANT: The single vector that results when two vectors are combined. 10m/s left 5m/s rt 5m/s left

6. Turn to the question on Page 17: A motor boat is moving 10 km/h relative to the water. If the boat travels in a river that flows at 10km/h, what is the velocity relative to the shore when it heads directly up stream? When it heads directly downstream?

7. Adding Noncollinear vectors The Pythagorean theorem is a useful method for determining the result of adding two (and only two) vectors which make a right angle to each other.

8. Graphical Vector Addition: A + B Step 1- Draw a start point. Step 2- Decide on a scale. Step 3- Draw Vector A to scale. Step 4- Vector B’s tail begins at Vector A’s head. Draw Vector B to scale. Step 5- Draw a line connecting the initial start point to the head of B. This is the resultant. Step 6- Measure the resultant’s length with a ruler and direction with a protractor. Step 7- Convert back to the given units using your scale.

9. Animation of head-to-tail vector addition – three times

10. Practice Graphical Addition Practice Set at The Physics Classroom

11. Resultants and Equilibrants The resultant is the vector sum of two or more vectors. It is the result of adding two or more vectors together. The equilibrant is the balancing vector… the vector equal in magnitude but opposite in direction to the resultant.

12. Vector Components Some vectors are directed at angles to the coordinate axes, and will need to be transformed into two parts with each part being directed along the axes. Each part of a two-dimensional vector is known as a component . Any vector directed in two dimensions can be thought of as having an influence in two different directions. The components of a vector depict the influence of that vector in a given direction.