MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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9.1 Vectors in Two Dimensions

Add and scale two-dimensional vectors.

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Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Components and magnitudeWorked steps · five questions02Vector operationsWorked steps · five questions03Unit vectorsWorked steps · five questions04Magnitude and direction formWorked steps · five questions05Applications: velocity and forceWorked steps · five questions
Lesson brief and rules

9.1 Vectors in Two Dimensions

Add vector components separately: ⟨a,ba,b⟩ ++ ⟨c,dc,d⟩ == ⟨a+c,b+da+c,b+d⟩. Multiply each component by a scalar.

Remember
Magnitude of ⟨a,b⟩ is √(a²+b²).
Worked example 11
01 / ⟨1,21, 2⟩ ++ ⟨3,−13, -1⟩ == ⟨4,14, 1⟩
Worked example 2 · Add vectors componentwise

Add ⟨2,−32, -3⟩ and ⟨4,54, 5⟩.

Add corresponding coordinates: ⟨2+4,−3+52 + 4, -3 + 5⟩ == ⟨6,26, 2⟩.

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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