Vector Addition & Subtraction

Discussion

introduction

text

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 (Σ), change (Δ)
dot product (·), cross 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
Mathematical quantities compared

Begin

Jump off the line.

More text

Don't forget the parallelogram rule.

Lot's of vectors to be added.

Conclude and get on with the sample problems.

special triangles

Some special triangles often found in standardized exam problems.

   

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.

45°, 45°, 90°
1 : 1 : √(2)

   

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.

30°, 60°, 90°
1 : 2 : √(3)

   

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.

37°, 53°, 90°
3 : 4 : 5

To summarize …


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