Vectors

Vectors A vector is a symbol that indicates both magnitude and direction. A vector quantity is one that is directional. Examples: Displacement Velocity Acceleration Force Notation: We will represent vector quantities like this: A scalar quantity only has magnitude, and does not depend on the direction. Examples: Distance Speed Temperature Notation: scalar quantities do not have an arrow above them. or

Vector addition and subtraction Example: displacement is a vector which represents the distance and direction between two points. Two vector quantities are added by placing the tail of the second vector at the head of the first vector. The negative of a vector has the same magnitude but points in the opposite direction.

Examples: Draw the vectors

Examples: Draw the vector

Adding and subtracting vectors http://surendranath.tripod.com/Applets/Math/VectorAddition/VectorAdditionApplet.html Addition is commutative and associative:

Components A vector component is the projection of that vector on an axis. Recall: right triangles: q

Examples of components Find the x and y components of the given vectors

Adding vectors by components http://surendranath.tripod.com/Applets/Math/VectorAddition/VectorAdditionApplet.html

Unit vectors We need some way to indicate the direction of a vector, independently of its magnitude. Define: are commonly used to denote unit vectors in the x,y and z directions, respectively