Pre-Calculus Chapter 6 Review Flashcards

Flashcards for Pre-Calculus Review Chapter 6

Component Form of a Vector

The component form of a vector represents the horizontal and vertical displacement from the initial point to the terminal point. It is found by subtracting the coordinates of the initial point from the coordinates of the terminal point.

Magnitude of a Vector

The magnitude of a vector is the length of the vector, calculated using the distance formula (or Pythagorean theorem) based on its component form.

Unit Vector

A vector with a magnitude of 1. It is found by dividing each component of the original vector by the magnitude of the original vector.

Direction Angle of a Vector

The angle, measured counterclockwise from the positive x-axis, to the vector. It can be found using trigonometric functions (arctan) based on the components of the vector.

Linear Combination of Standard Unit Vectors (i and j)

Expressing a vector as a sum of scalar multiples of the standard unit vectors i (horizontal component) and j (vertical component).

Dot Product of Vectors

A scalar value resulting from a specific operation on two vectors. For u = (u1, u2) and v = (v1, v2), the dot product u.v = u1v1 + u2v2.

Angle Between Two Vectors

The angle (θ) between two vectors u and v can be found using the formula: cos(θ) = (u.v) / (||u|| * ||v||), where u.v is the dot product of u and v, and ||u|| and ||v|| are the magnitudes of u and v, respectively.

Absolute Value of a Complex Number

The distance from the complex number to the origin in the complex plane. For a complex number a + bi, the absolute value is √(a^2 + b^2).

Trigonometric Form of a Complex Number

Representing a complex number z = a + bi as z = r(cos θ + i sin θ), where r is the magnitude (absolute value) of the complex number and θ is the argument (angle) of the complex number.