|definition||a quantity that has |
|a quantity that has both |
magnitude and direction
|up, down, left, right |
north, east, west, south
positive, negative (in a coordinate system)
angle of inclination, depression
angle with the vertical, horizontal
right ascension, declination
proper time (relativistic)
electric, magnetic, gravitational fields
|mathematics||"ordinary" arithmetic |
|vector arithmetic |
vector addition, vector subtraction
resultant (Σ), change (Δ)
dot product (·), cross product (×)
|answers||a number with a unit||a number with a unit and a direction angle |
a number with a unit along each coordinate axis
an arrow drawn to scale in a specific direction
- Parallel vectors behave like numbers on a number line.
- Add the magnitudes of vectors in the same direction.
- Subtract the magnitudes of vectors in opposite directions.
Jump off the line.
- Perpendicular vectors behave like points on a coordinate plane.
- Use Pythagorean theorem to determine magnitude.
- Use the tangent function to determine direction.
- Vectors can be arranged…
- in standard position or
- head to tail.
Don't forget the parallelogram rule.
- Parallelogram Rule.
Lots of vectors to be added.
- Vector addition is similar to arithmetic addition.
- Vector addition is a binary operation. (Only two vectors can be added at a time.)
- Vector addition is commutative. (The order of addition is unimportant.)
Conclude and get on with the sample problems.