Discussion

introduction

text

Quantities Compared
aspect	scalars	vectors
definition	a quantity that has magnitude only	a quantity that has both magnitude and direction
		up, down, left, right north, east, west, south forward, backward parallel, perpendicular positive, negative (in a coordinate system) bearing angle angle of inclination, depression angle with the vertical, horizontal right ascension, declination
examples	distance mass time (classical) surface area volume density speed energy	displacement weight proper time (relativistic) projected area velocity acceleration force momentum electric, magnetic, gravitational fields
mathematics	"ordinary" arithmetic addition, subtraction sum, difference multiplication	vector arithmetic vector addition, vector subtraction resultant (net), change (delta) dot (scalar) product, cross (vector) product
answers	a number with a unit	a number with a unit and a direction angle -or- a number with a unit along each coordinate axis -or- an arrow drawn to scale in a specific direction

Begin

• 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 Pythagoras' theorem to determine magnitude.
  • Use tangent to determine direction.

More text

• Vectors can be arranged …
  • in standard position or
  • head to tail.

Don't forget the parallelogram rule.

• Parallelogram Rule.

Lot's 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.

special triangles

45°, 45°, 90° 1 : 1 : √(2)		An isosceles right triangle. The two legs are equal in size. If we assume each leg has a length of one, according to Pythagoras' theorem, the hypotenuse has a length equal to the square root of two.
30°, 60°, 90° 1 : 2 : √(3)		Half an equilateral triangle. Assume the sides of the full triangle have a length of two. Split it in half and the side opposite the 30° angle has a length of one. Using Pythagoras' theorem, the remaining leg has a length equal to the square root of three.
37°, 53°, 90° 3 : 4 : 5		The simplest Pythagorean triple. The size of the angles are best determined with a calculator. Standardized tests love this triangle. (Secret reason: It simplifies grading.) Some people memorize these angles to help them spot 3-4-5 triangles on tests.

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