Review of Vector Algebra - EMF
Scalar and Vector Quantities in Music
Four Basic Operations with Vectors
When dealing with vectors in music, there are four basic
operations that can be performed:
1. Addition: Two vectors can be added together to create a
resultant vector. This is done by combining the individual
components of each vector.
2. Subtraction: One vector can be subtracted from another
to find the difference between them. This is done by
subtracting the individual components of one vector from
the other.
3. Multiplication: A vector can be multiplied by a scalar (a
single number) to change its magnitude (length) without
changing its direction.
4. Division: A vector can be divided by a scalar to reduce its
magnitude without changing its direction.
Vector Components and Parallelogram Law
A vector can be broken down into its component parts,
which are vectors that point in the x and y directions.
These components can be used to add and subtract
vectors using the parallelogram law.
The parallelogram law states that if two vectors are
represented as adjacent sides of a parallelogram, the
diagonal of the parallelogram represents the resultant
vector. This can be used to add and subtract vectors both
graphically and algebraically.
Scalar and Vector Quantities in Music
Four Basic Operations with Vectors
When dealing with vectors in music, there are four basic
operations that can be performed:
1. Addition: Two vectors can be added together to create a
resultant vector. This is done by combining the individual
components of each vector.
2. Subtraction: One vector can be subtracted from another
to find the difference between them. This is done by
subtracting the individual components of one vector from
the other.
3. Multiplication: A vector can be multiplied by a scalar (a
single number) to change its magnitude (length) without
changing its direction.
4. Division: A vector can be divided by a scalar to reduce its
magnitude without changing its direction.
Vector Components and Parallelogram Law
A vector can be broken down into its component parts,
which are vectors that point in the x and y directions.
These components can be used to add and subtract
vectors using the parallelogram law.
The parallelogram law states that if two vectors are
represented as adjacent sides of a parallelogram, the
diagonal of the parallelogram represents the resultant
vector. This can be used to add and subtract vectors both
graphically and algebraically.
