Scalars and Vectors – Key Vocabulary

Vocabulary flashcards covering fundamental terms and principles related to scalars, vectors, their representation, and operations from the provided lecture notes.

Scalar

A quantity that possesses magnitude only, with no associated direction.

Vector

A quantity that possesses both magnitude and direction.

Scalar Quantity

Any measurable property described solely by a number and unit (e.g., mass, temperature, time).

Vector Quantity

Any measurable property described by both a number (magnitude) and a specific direction (e.g., force, velocity).

Displacement

A vector representing the straight-line change in position, including magnitude and direction.

Force (or Weight)

A vector quantity that describes a push or pull acting on an object, expressed in newtons.

Velocity

A vector that specifies the rate of change of position and its direction of motion.

Acceleration

A vector that specifies the rate of change of velocity with respect to time.

Moment (Torque)

A vector representing the tendency of a force to cause rotation about an axis.

Vector Arrow

Graphical representation of a vector; arrow length indicates magnitude, arrowhead shows direction.

Vector Diagram

A sketch using arrows to represent vectors and their relationships, often forming triangles for analysis.

Resultant Vector

The single vector that has the same overall effect as two or more combined vectors.

Right-Angle Triangle

A triangle containing a 90° angle; used in vector resolution and trigonometry.

Pythagoras’ Theorem

For a right-angle triangle, hypotenuse² = adjacent² + opposite² (c² = a² + b²).

Sine Ratio (sin θ)

In a right-angle triangle, sin θ = opposite / hypotenuse.

Cosine Ratio (cos θ)

In a right-angle triangle, cos θ = adjacent / hypotenuse.

Tangent Ratio (tan θ)

In a right-angle triangle, tan θ = opposite / adjacent.

Component of a Vector

The projection of a vector onto a chosen axis, giving perpendicular x and y parts.

x-Component (aₓ)

The horizontal part of a vector, found with aₓ = |a| cos θ.

y-Component (a_y)

The vertical part of a vector, found with a_y = |a| sin θ.

Magnitude (|a⃗|)

The length or size of a vector, often obtained with √(aₓ² + a_y²).

Direction (θ)

The angle a vector makes with a reference axis, commonly found with tan⁻¹(opposite/adjacent).

Unit Vector

A vector of length 1 used to specify direction; î for x-axis, ĵ for y-axis.

Complex Form of a Vector

Representation using unit vectors: A⃗ = Aₓ î + A_y ĵ.

Cartesian Form

Ordered-pair notation of a vector: (x, y).

Polar Coordinates

Representation of a vector by its magnitude and direction: (r, θ).

Commutative Law of Vector Addition

A⃗ + B⃗ = B⃗ + A⃗; order does not affect the sum.

Associative Law of Vector Addition

A⃗ + (B⃗ + C⃗) = (A⃗ + B⃗) + C⃗; grouping does not affect the sum.

Adding Vectors by Components

Process of summing corresponding x and y components to obtain the resultant.

Subtracting Vectors by Components

Process of subtracting corresponding x and y components to find the difference.