Vectors and Coordinate Systems

Flashcards covering key vocabulary terms from the lecture on Vectors and Coordinate Systems.

Vector Quantity

A quantity that includes both magnitude (always positive) and direction (e.g., displacement and velocity).

Magnitude (of a vector)

The always positive numerical value of a vector quantity.

Direction (of a vector)

The orientation or path of a vector quantity.

Displacement

A straight-line connection from an initial position to a final position, with its magnitude being the straight-line distance between the two positions.

Equal Vectors

Two vectors that have the same magnitude and direction, even if their arrows have different starting and ending points.

Vector Addition

The process of graphically combining successive displacements or any two vectors to produce an overall resultant vector.

Commutative Property of Vector Addition

The property stating that vectors can be added in any order (A + B = B + A) and yield the same resultant vector.

Resultant Vector

The single vector that represents the sum of two or more vectors, drawn from the free tail to the free head when vectors are laid head-to-tail.

Scalar Multiplication (positive scalar)

Multiplying a vector by a positive scalar, which results in a vector of a different magnitude pointing in the same direction.

Scalar Multiplication (by -1)

Multiplying a vector by -1, which reverses its direction while leaving its magnitude unchanged.

Vector Subtraction

The process of adding the negative of the vector to be subtracted (by flipping its direction) to the other vector.

Component Vectors

Vectors that are parallel to the coordinate axes and add together to give the original vector.

Component (of a vector)

The magnitude of a corresponding component vector, with a sign to indicate its direction.

Unit Vectors

Vectors of magnitude 1 used conveniently to express the components of any vector, typically denoted as i-hat (x-direction), j-hat (y-direction), and k-hat (z-direction).

i-hat (î)

The unit vector in the positive x-direction.

j-hat (ĵ)

The unit vector in the positive y-direction.

k-hat (k̂)

The unit vector in the positive z-direction.

Algebraic Vector Addition

A method of adding vectors by treating unit vectors as algebraic variables, grouping similar terms (components) for separate addition.

Vector Equation

A shorthand notation representing a set of separate equations for each component (e.g., x, y, and z components) of the vectors involved.