CurriculumGrade 12Mathematics

Adding and Subtracting Vectors

Aligned to N-VM.B.4 — Common Core State Standards for Mathematics.

What this lesson teaches

This is a (+) advanced standard. Add vectors component-wise: <a, b> + <c, d> = <a + c, b + d>. The magnitude of the sum is usually not the sum of the magnitudes. Scalar multiplication k<a, b> = <ka, kb> scales the length by |k|.

Worked example

Add <3, 4> + <1, −1> = <4, 3>. The magnitude of this sum is √(4^2 + 3^2) = √25 = 5, which is not 5 + √2 (the sum of the two lengths).

Practice questions

  1. Add <2, 5> + <3, −2>.
  2. Compute the scalar multiple 3<1, −4>.
  3. Find <6, 8> − <2, 5> 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

Sumar y restar vectores

Este es un estándar avanzado (+). Suma vectores componente por componente: <a, b> + <c, d> = <a + c, b + d>. La magnitud de la suma normalmente no es la suma de las magnitudes. La multiplicación por un escalar k<a, b> = <ka, kb> escala la longitud por |k|.

Ejemplo: Suma <3, 4> + <1, −1> = <4, 3>. La magnitud de esta suma es √(4^2 + 3^2) = √25 = 5, que no es 5 + √2 (la suma de las dos longitudes).

More Number & Quantity lessons

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

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