Vectors
Vectors that are added must be drawn...
"tip-to-tail"
If vector a equals axî+ayĵ+azk and vector b equals bxî+byĵ+bzk, then vector a crossed with vector b equals...
(aybz-azby)î + (azbx-axbz)ĵ + (axby-aybx)k
The cross product of unit vector j crossed with unit vector k is...
+unit vector i
The cross product of unit vector k crossed with unit vector i is...
+unit vector j
The cross product of unit vector i crossed with unit vector j is...
+unit vector k
The cross product of unit vector k crossed with unit vector j is...
-unit vector i
The cross product of unit vector i crossed with unit vector k is...
-unit vector j
The cross product of unit vector j crossed with unit vector i is...
-unit vector k
True/False: The length of each vector added together is equal to the length of the overall displacement.
FALSE
True/False: The order that vectors are multiplied using the cross product does NOT matter.
False
True/False: Vectors of the different types can be added together.
False: only vectors of the same type can be added together
The result of multiplying a vector by a scalar is...
a new vector
vector
a number with direction
scalar
a number without direction
The dot product of two vectors results in...
a scalar
unit vector
a vector with a magnitude of 1
When multiplying a vector by a vector, the scalar (dot) product is equal to...
abcos(theta)
If vector a crossed with vector b equals vector c, then vector c is equal to...
absin(theta)
adding vectors in unit vector notation
add the corresponding components (answer will be written in unit vector notation or can be converted to magnitude-angle notation)
The difference of two vectors is the same as...
adding the negative of the second vector
If there are more than 2 vectors being added together, they (can/cannot) be grouped in any order.
can
unit vector notation
describes vectors by breaking them into there x, y and z components and are denoted by "i-hat", "j-hat" and "k-hat" respectively
The order vectors are added in (does/does not) matter.
does not
Dividing a vector by a scalar is the same as...
multiplying by 1 over the scalar
When multiplying a vector by a scalar, the direction of a new vector is the opposite if vector a is...
negative
The scalar (dot) product multiplies that part of vector a and vector b that are...
parallel
The cross product multiplies that part of vector a and vector b that are...
perpendicular
When multiplying a vector by a scalar, the direction of a new vector is the same if vector a is...
positive
component notation
projections of a vector along the axes of a coordinate system (x, y, and/or z components)
Putting a negative sign in front of a vector ... its direction, but (does/does not) change its magnitude.
reverse its direction does not
The way we get the direction of vector c (which is the cross product of vectors a and b) is to use...
the right-hand rule (RHR)
The dot product of two vectors in unit-vector notation is equal to...
the x component of a times that x component of b plus the y component of a times that y component of b plus the z component of a times that z component of b
The cross product of two vectors results in a (vector/scalar)
vector
magnitude-angle notation
vector a = a @ theta degrees North of East
When is vector a crossed with vector b a minimum magnitude?
when theta=0 degrees (sin0=0) so when vector a and vector b are parallel
When is vector a crossed with vector b a maximum magnitude?
when theta=90 degrees (sin90 = 1)
When is the scalar (dot) product of vector a and vector b a maximum?
when vector a and vector b are parallel or antiparallel (theta is 0 or 180 and the cos equals 1 or -1)
When is the scalar (dot) product of vector a and vector b a minimum?
when vector a and vector b are perpendicular (theta is 90 and the cos equals 0)
Can a scalar be positive or negative? Do the signs indicate direction?
yes no (signs DO NOT indicate direction)
Can a vector be positive or negative? Do the signs indicate direction?
yes yes (signs DO indicate direction)
