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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9.2 The Dot Product

Focus on dot product and dot product calculation.

Before you solve

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.

01Computing the dot productWorked steps · five questions02Angle between vectorsWorked steps · five questions03Orthogonal vectorsWorked steps · five questions04Projection and workWorked steps · five questions
Lesson brief and rules

9.2 The Dot Product

⟨a,ba,b⟩⋅\cdot ⟨c,dc,d⟩=ac+=ac+ bd; a zero dot product means perpendicular nonzero vectors.

Worked example 11
01 / Find ⟨3,53,5⟩⋅\cdot ⟨4,74,7⟩.
02 / Multiply matching components and add: 12+35=4712+35=47.
03 / Answer: 4747
Worked example 2 · Dot product calculation

Find ⟨4,64,6⟩⋅\cdot ⟨1,−11,-1⟩.

Multiply corresponding components and add: 4−64-6. Answer: −2-2

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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