The document discusses vectors, including defining scalars and vectors, representing vectors using common direction, polar and rectangular coordinates, finding the resultant of adding or subtracting vectors graphically or analytically, resolving vectors into components, and examples of adding and subtracting vectors by changing their magnitudes and directions. Key concepts covered include finding components, conversions between polar and rectangular coordinates, using the Pythagorean theorem and trigonometric functions to solve for vectors, and the differences between adding and subtracting vectors.

1. Vectors

2. Vectors
Surveyors use accurate measures of
magnitudes and directions to create
scaled maps of large regions.

3. Review:
1. What is a scalar?
2. Give some examples of scalars.
3. What is a vector?
4. Give some examples of vectors.
5. How do you represent a vector?
6. What is the denotation (how do
you write) of a vector?

4. Review: Writing a vector
1. Common direction
2. Polar coordinate
3. Rectangular coordinate

5. Review: Resultant
1. What is a resultant?
2. Finding the resultant using graphical
solution.

6. Analytical Vector Resolution:
Co-linear Vectors

7. Analytical Vector Resolution (cont…)
1. Triangle method – for adding/subtracting TWO
vectors.
The Pythagorean Theorem and SohCahToa:

8. Components of Vectors
A component is the effect of a vector along other
directions. The x and y components of the vector
are illustrated below.
Finding components:
Polar to Rectangular
Conversions
The Pythagorean Theorem
and SohCahToa:

10. Addition and Subtraction
Subtraction results in a significant difference
both in the magnitude and the direction of
the resultant vector. |(A – B)| = |A| - |B|
Comparison of addition and subtraction of B
R=A+B R’ = A - B
B
A
R
B R’ -B
A A

11. Sample Problem:
Polar Angle
140 -11.5 9.6
180 25.0 0
210 -15.6 -9.0
-2.1 0.6