Skill 9: Vectors and Vector Operations

Vocabulary flashcards covering vector concepts, vector component formulas, head-to-toe vector addition, scalar multiplication, and quadrant signs based on Skill 9 notes.

Scalar

A physical quantity that has magnitude (size) only, such as mass or time.

Vector

A physical quantity that has both magnitude (size) and direction, such as force or velocity.

Vector Components

The horizontal and vertical parts of a vector that lie along the perpendicular x-axis and y-axis.

Horizontal Component ($A_x$)

The part of vector $A$ lying along the x-axis, calculated as $A_x = A \tan(\theta)$ if measured from vertical, or $A_x = A \times \text{cos}(\theta)$ when angle $\theta$ is measured from the x-axis.

Vertical Component ($A_y$)

The part of vector $A$ lying along the y-axis, calculated as $A_y = A \times \text{sin}(\theta)$ when angle $\theta$ is measured from the x-axis.

Pythagorean Theorem for Vectors

The relationship $A_x^2 + A_y^2 = A^2$ used to determine the magnitude of a vector $A$ from its perpendicular components.

Inverse Tangent for Vector Angle

The relationship \theta = \tan^{-1}\theta\right(\frac{A_y}{A_x}\right) used to determine the angle $\theta$ of a vector based on its vertical and horizontal components.

Quadrant Signs of Vector Components

The rule determining whether x and y components are positive or negative based on the quadrant: Quadrant 1 ($+$, $+$), Quadrant 2 ($-$, $+$), Quadrant 3 ($-$, $-$), and Quadrant 4 ($+$, $-$).

Head-to-Toe Vector Addition

A graphical method of adding vectors where the second vector is drawn starting at the end (head) of the first vector, and the resultant vector is drawn from the starting point to the final end point.

Vector Subtraction

The process of subtracting a vector by adding a vector that has an equal magnitude but points in the opposite direction.

Scalar Multiplication of a Vector

The process of multiplying a vector by a scalar, which scales the vector's length by the scalar factor and flips its direction if the scalar is negative.