Journal Entry 7 Vector Analysis

Vectors are used to represent the value and direction of some quantity. The length of the vector represents its value, or magnitude. The arrowhead shows its direction. Scalars to not have direction, only a magnitude.

Vector Quantities Position Displacement Velocity Force Weight Acceleration Momentum Torque Scalar Quantities Distance Speed Time Mass Volume Energy Work Temperature

A vector existing in multiple dimensions can be split into components. Each component represents the magnitude of the vector within that dimension.

Vector addition is the process of combining multiple vectors to produce a new vector, called the resultant. Vectors that exist in the same dimension can be combined with simple addition or subtraction. + = -10 +10 +4 +7 +11 + = +20

The “pieces” of the combined vector are called components. Vectors that exist in different dimensions must be combined using geometry. + = Resultant Horizontal Component Vertical Component The “pieces” of the combined vector are called components.

A resultant vector can be resolved into its components, provided the both the vector’s magnitude and direction are known. Trigonometry required to resolve a vector. Vx = vcos(θ) Vy = vsin(θ)

When drawing vectors, use the origin of a coordinate plane as reference. Draw vectors “head to tail”. Connect the tail of the first vector to the head of the last vector to draw the resultant. This is called…the “head to tail” method.

When using cardinal directions (NSEW), pay careful attention to the angle you assign to a resultant vector.

DO NOT LEAVE THIS SLIDE BLANK!