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Introduction to vectors
vector notation and operations
by
TweetDavid Strasburger
on 11 October 2016Transcript of Introduction to vectors
Vectors
are quantities with magnitude and direction
how do we indicate that a quantity is vectorvalued?
how is a vector specified?
directionmagnitude form
Vector Operations:
addition
subtraction
magnitude
multiplication by scalar
dot product
cross product
"5, 53° north of east"
components, ordered pair, unitvector form
how long is this vector?
directionmagnitude form
"5, 53° north of east"
components, ordered pair, unitvector form
Notation:
Vector
Formalism
Representation:
http://drifters.doe.gov/trackayoto/trackadrifter.html
http://en.wikipedia.org/wiki/File:3D_Spherical_2.svg
if vectors a and b were placed tiptotail, what vector would go from the tail of the first to the tip of the second?
graphical interpretation
graphical interpretation
magnitude
addition
subtraction
multiplication by scalar
dot product
cross product
directionmagnitude form
questions
is addition commutative? can you prove it?
is it associative? can you prove it?
¿
questions
What happens if the scalar is negative?
Is multiplication by a scalar associative?
how can you use multiplication by scalar to create a unit vector?
such as rhat in gravitation or Coulomb
¿
by components
if vectors a and b were placed tailtotail, what vector would go from the tip of the first to the tip of the second?
graphical interpretation
directionmagnitude form
by components
questions
is subtraction commutative? can you prove it?
¿


questions
¿
How much do these two vectors point in the same direction?
graphical interpretation
directionmagnitude form
by components
graphical interpretation
directionmagnitude form
by components
graphical interpretation
directionmagnitude form
by components
also called "the scalar product"
Is the dot product commutative?
What does it mean if the dot product is negative?
Can the dot product be zero if both vectors have nonzero magnitudes?
How can you use the dot product to find the included angle?
How much are these two vectors perpendicular?
also called "the vector product"
magnitude:
direction:
by righthand rule
questions
¿
Is the cross product commutative?
Can the cross product of nonzero vectors be zero?
Full transcriptare quantities with magnitude and direction
how do we indicate that a quantity is vectorvalued?
how is a vector specified?
directionmagnitude form
Vector Operations:
addition
subtraction
magnitude
multiplication by scalar
dot product
cross product
"5, 53° north of east"
components, ordered pair, unitvector form
how long is this vector?
directionmagnitude form
"5, 53° north of east"
components, ordered pair, unitvector form
Notation:
Vector
Formalism
Representation:
http://drifters.doe.gov/trackayoto/trackadrifter.html
http://en.wikipedia.org/wiki/File:3D_Spherical_2.svg
if vectors a and b were placed tiptotail, what vector would go from the tail of the first to the tip of the second?
graphical interpretation
graphical interpretation
magnitude
addition
subtraction
multiplication by scalar
dot product
cross product
directionmagnitude form
questions
is addition commutative? can you prove it?
is it associative? can you prove it?
¿
questions
What happens if the scalar is negative?
Is multiplication by a scalar associative?
how can you use multiplication by scalar to create a unit vector?
such as rhat in gravitation or Coulomb
¿
by components
if vectors a and b were placed tailtotail, what vector would go from the tip of the first to the tip of the second?
graphical interpretation
directionmagnitude form
by components
questions
is subtraction commutative? can you prove it?
¿


questions
¿
How much do these two vectors point in the same direction?
graphical interpretation
directionmagnitude form
by components
graphical interpretation
directionmagnitude form
by components
graphical interpretation
directionmagnitude form
by components
also called "the scalar product"
Is the dot product commutative?
What does it mean if the dot product is negative?
Can the dot product be zero if both vectors have nonzero magnitudes?
How can you use the dot product to find the included angle?
How much are these two vectors perpendicular?
also called "the vector product"
magnitude:
direction:
by righthand rule
questions
¿
Is the cross product commutative?
Can the cross product of nonzero vectors be zero?