University:
York University
Course:
MATH 1013 | Applied Calculus
Academic year:

2023
Views:

92

Pages:

1
Author:

Niklas

III. Vectors I. VECTORS A vector is a quantity that has magnitude and direction. NOTATION: A vector is a directed line segment on the plane. Examples of vectors: [Diagram of two vectors] Example of a vector in standard position: [Diagram of a vector in standard position] COMPONENT FORM: The component form of the vector with initial point P(p1,p2) and terminal point Q(q1,q2) is given by: PQ = = y/v When a vector is in standard position, it can be described uniquely by the coordinates of its terminal point, (v1,v2). This is the component form of v: v = . II. FIND THE MAGNITUDE AND DIRECTION The magnitude is given by: ||v|| = sqrt(v1^2 + v2^2) The direction angle is given by: tan(θv) = v2/v1 Examples: Given v = <1,5>, determine ||v|| and θv. ||v|| = sqrt(1^2 + 5^2) ≈ 5.16 tan(θv) = 5/1 θv = tan^-1(5) ≈ 79° Given A(-1,2) and B(-4,4), determine ||AB|| and θAB. AB = <-2,2> ||AB|| = sqrt((-2)^2 + 2^2) = 2√2 ≈ 2.83 tan(θAB) = 2/-2 θAB = tan^-1(-1) + 180° ≈ 135°