Vector Physics Lesson 2 by Owen Borville 11.13.2025
Vectors are quantities that have both magnitude and direction, such as displacement or velocity.
Scalars are quantities that have magnitude only and no direction.
Vectors are represented by arrows placed above the variable. The length of the vector is its magnitude. Two vectors are equal if they have the same magnitude and direction. Multiplying a vector by a scalar value only changes the length of the vector.
Multiplication does not change the direction of the vector, unless the scalar is negative, which would reverse the original direction.
Vectors can be added to other vectors, subtracted to other vectors, and multiplied. The sum of two vectors is the resultant vector. Scalars can be added.
Vectors cannot be added to scalars.
Parallelogram method is used to add two vectors.
Tail-to-head method is used to add multiple vectors.
Vectors can be divided by non-zero scalars but not by vectors.
Vectors have two components in two dimensions. Vectors have three components in three dimensions.
Products (multiplication) of vectors: with scalar = scalar product or dot product distributive property and communicative property
Products (multiplication) of vectors: with vectors = vector product or cross product distributive property and anti-communicative property (when multiplication order changes, the result is a minus sign)
Scalar product of two vectors: multiply magnitudes with the cosine of the angle between them.
The scalar product of antiparallel vectors is negative (-).
Vector product of two vectors is a vector perpendicular to both of them. The magnitude is found by multiplying the magnitudes of the sine of the angle between them.
Direction of vector product: corkscrew right-hand rule. The vector product of two parallel or antiparallel vectors vanishes. The magnitude of the vector product is largest for orthogonal vectors.
The scalar product of vectors is used to find angles between vectors and in the definitions of derived scalar physical quantities such as work or energy.
The cross product of vectors is used in definitions of derived vector physical quantities such as torque or magnetic force, and in describing rotations.
Vectors are quantities that have both magnitude and direction, such as displacement or velocity.
Scalars are quantities that have magnitude only and no direction.
Vectors are represented by arrows placed above the variable. The length of the vector is its magnitude. Two vectors are equal if they have the same magnitude and direction. Multiplying a vector by a scalar value only changes the length of the vector.
Multiplication does not change the direction of the vector, unless the scalar is negative, which would reverse the original direction.
Vectors can be added to other vectors, subtracted to other vectors, and multiplied. The sum of two vectors is the resultant vector. Scalars can be added.
Vectors cannot be added to scalars.
Parallelogram method is used to add two vectors.
Tail-to-head method is used to add multiple vectors.
Vectors can be divided by non-zero scalars but not by vectors.
Vectors have two components in two dimensions. Vectors have three components in three dimensions.
Products (multiplication) of vectors: with scalar = scalar product or dot product distributive property and communicative property
Products (multiplication) of vectors: with vectors = vector product or cross product distributive property and anti-communicative property (when multiplication order changes, the result is a minus sign)
Scalar product of two vectors: multiply magnitudes with the cosine of the angle between them.
The scalar product of antiparallel vectors is negative (-).
Vector product of two vectors is a vector perpendicular to both of them. The magnitude is found by multiplying the magnitudes of the sine of the angle between them.
Direction of vector product: corkscrew right-hand rule. The vector product of two parallel or antiparallel vectors vanishes. The magnitude of the vector product is largest for orthogonal vectors.
The scalar product of vectors is used to find angles between vectors and in the definitions of derived scalar physical quantities such as work or energy.
The cross product of vectors is used in definitions of derived vector physical quantities such as torque or magnetic force, and in describing rotations.