The Physics
Hypertextbook
Opus in profectus

Vector Addition & Subtraction

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Summary

Physical quantities compared
aspect scalars vectors
definition a quantity that has
magnitude only
a quantity that has both
magnitude and direction
directions   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
uptown, downtown, crosstown
etc.
examples distance
time (classical)
speed
 
 
mass
energy
surface area
volume
density
displacement
proper time (relativistic)
velocity
acceleration
force
weight
momentum
projected area
fields higgs field gravitational field, electromagnetic field, strong nuclear field, weak nuclear field
mathematics arithmetic:
addition, subtraction
sum, difference
multiplication
trigonometry:
vector addition, vector subtraction
resultant or net (Σ), change (Δ)
dot product (·), cross product (×)
answers a number with a unit a number and a direction angle, both with units
-or-
a number with a unit for each unit vector ()
-or-
an arrow drawn to scale in a specific direction