CurriculumGrade 12Mathematics

Finding Vector Components

Aligned to N-VM.A.2 — Common Core State Standards for Mathematics.

What this lesson teaches

A vector from an initial point P to a terminal point Q has components found by subtracting coordinates: <Qx − Px, Qy − Py>. These give the horizontal and vertical change.

Worked example

From P(1, 2) to Q(4, 6), the components are <4 − 1, 6 − 2> = <3, 4>. Its magnitude is √(3^2 + 4^2) = √25 = 5.

Practice questions

  1. Find the components of the vector from (0, 0) to (5, −2).
  2. Find the components of the vector from P(−3, 1) to Q(2, 4).
  3. Find the vector from (7, 3) to (1, 3) and its magnitude.

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Hallar las componentes de un vector

Un vector que va de un punto inicial P a un punto terminal Q tiene componentes que se hallan restando coordenadas: <Qx − Px, Qy − Py>. Estas dan el cambio horizontal y vertical.

Ejemplo: De P(1, 2) a Q(4, 6), las componentes son <4 − 1, 6 − 2> = <3, 4>. Su magnitud es √(3^2 + 4^2) = √25 = 5.

More Number & Quantity lessons

Adding and Multiplying Complex NumbersN-CN.A.2Quadratics with Complex SolutionsN-CN.C.7The Fundamental Theorem of AlgebraN-CN.C.9Adding and Subtracting VectorsN-VM.B.4Representing Data with MatricesN-VM.C.6Matrix Addition and MultiplicationN-VM.C.8

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