Scalars and Vectors Flashcards

This set of vocabulary flashcards defines the fundamental concepts of scalars and vectors, their types, properties, and the operations of addition and multiplication based on the lecture material.

Scalar

A physical quantity that has only a magnitude, such as mass, length, time, and temperature.

Vector

A physical quantity that has both a magnitude and a direction, such as position, displacement, velocity, and force.

Parallel Vectors

Two vectors are said to be parallel if they have the same direction.

Equal Vectors

Two parallel vectors are said to be equal vectors if they have the same magnitude ($A = B$).

Anti-parallel Vectors

Two vectors are said to be anti-parallel if they are in opposite directions.

Negative Vectors

Two anti-parallel vectors are said to be negative vectors if they have the same magnitude ($A = -B$).

Collinear Vectors

Two vectors that act along the same line.

Co-initial Vectors

Two or more vectors that have a common initial point.

Co-terminus Vectors

Two or more vectors that have a common terminal point.

Coplanar Vectors

Three or more vectors that lie in the same plane.

Non-coplanar Vectors

Three or more vectors that are distributed in space.

Polar Vectors

Vectors having a straight line effect, such as Displacement, Velocity, Acceleration, and Force.

Axial Vectors

Vectors having a rotational effect, such as Angular momentum, Angular velocity, Angular acceleration, and Torque.

Commutative Property

A property of vector addition stating that the order of addition does not matter: $A + B = B + A$.

Associative Property

A property of vector addition stating that $(A + B) + C = A + (B + C)$.

Magnitude of Resultant (Analytical)

The magnitude calculation for the resultant of two vectors $P$ and $Q$ with angle $\theta$: $R = \text{square root of } P^2 + 2PQ \times \text{cos}(\theta) + Q^2$.

Unit Vector

A vector that has a magnitude of exactly $1$ and is used to specify a direction in space; it lacks both dimension and unit.

Resolution of a Vector

The process of splitting a vector into two or more vectors such that their combined effect is the same as that of the given vector.

Scalar Product (Dot Product)

A way to multiply vectors that produces a scalar quantity: $A \cdot B = AB \cos(\theta)$, like Work ($W = F \cdot s$) and Power ($P = F \cdot v$).

Vector Product (Cross Product)

A way to multiply vectors that produces a vector quantity: $A \times B = AB \sin(\theta) \hat{n} = C$, representing the area of a parallelogram.

Cartesian Unit Vectors

Specific unit vectors along the axes: $\hat{i}$ for x, $\hat{j}$ for y, and $\hat{k}$ for z.