Vectors

We will start with a basic review of vectors.

Recall: We can add vectors graphically. a b a b a+b

However an easier way is to add components. Recall that any vector can be written as x and y components:

However an easier way is to add components. Recall that any vector can be written as x and y components: where and

Important concepts in vectors

Adding vectors by components Assume two vectors:

Adding vectors by components Assume two vectors: The sum of the two vectors is:

Example Consider the vectors: Then,

Dot Product (Scalar product) The dot product between two vectors is defined as: The smallest angle between the vectors a b

Dot Product (Scalar product) The dot product between two vectors is defined as: In unit vector notation: The smallest angle between the vectors a b

Dot Product (Scalar product) The scalar produce of two vectors is a scalar!

Example Find the scalar product of the vectors,

Example Find the scalar product of the vectors,

Vector Product (Cross product) The vector product between two vectors is defined as: The cross product of two vectors is a vector which is perpendicular to the plane of the vectors a and b. a b

Vector Product (Cross product) The direction of the resultant vector is given by the right hand rule. a b Using the right hand the fingers curl from the vector a to b while the thumb points in the direction of the resultant vector

Vector Product (Cross product) The direction of the resultant vector is given by the right hand rule. In unit vector notation: a b Using the right hand the fingers curl from the vector a to b while the thumb points in the direction of the resultant vector