Vector Algebra

These flashcards cover key concepts and definitions related to vector algebra as discussed in the lecture.

Vector quantity

A physical quantity expressed in a coordinate system that has both magnitude and direction, such as velocity.

Parallel vectors

Two vectors that have the same direction.

Equal vectors

Two vectors that have the same magnitude and same direction regardless of their position in space.

Negative of a vector

A vector with the same magnitude as the original vector but in the opposite direction.

Antiparallel vector

Vectors that have opposite directions, regardless of their magnitudes.

Commutative Law for Addition

States that A + B = B + A for any vectors A and B.

Associative Law for Addition

States that (A + B) + C = A + (B + C) for any vectors A, B, and C.

Scalar Distributive Law

States that p(A + B) = pA + pB, where p is a scalar and A and B are vectors.

Vector sum

The result of adding two or more vectors together.

Components of a vector

The projections of a vector onto the axes of a coordinate system, typically defined in terms of x and y components.

Magnitude of a vector

The length or size of the vector, represented mathematically as |A|.

Pythagorean Theorem in vector addition

The relationship |A| = √(Ax² + Ay²) used to find the magnitude of the resultant vector from its components.

Direction of a vector

The angle at which the vector is oriented with respect to a reference direction, usually measured from the positive x-axis.

Resultant displacement

The total displacement resulting from two or more vector displacements.

Head-to-Tail method

A graphical method of adding vectors by placing the tail of one vector at the head of the previous vector.

Parallelogram method

A graphical method of vector addition where two vectors are represented as adjacent sides of a parallelogram.