The Physics
Hypertextbook
Opus in profectus

# Vector Addition & Subtraction

## Discussion

### introduction

text

Mathematical 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 (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

### 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 Pythagorean theorem to determine magnitude.
• Use the tangent function to determine direction.

More text

• 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.