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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9.4 Vectors in Three Dimensions

Focus on vector addition and magnitude.

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.

01Vectors in spaceWorked steps · five questions02Dot product and direction angles in spaceWorked steps · five questions
Lesson brief and rules

9.4 Vectors in Three Dimensions

Add corresponding x,yx, y, and zz components.

Worked example 11
01 / Find ⟨3,5,43,5,4⟩++⟨7,10,37,10,3⟩.
02 / Add each of the three matching components.
03 / Answer: ⟨10,15,710,15,7⟩
Worked example 2 · Magnitude

Find ∣|⟨12,16,012,16,0⟩∣|.

Use x2+y2+z2=5a\sqrt{x^{2}+y^{2}+z^{2}}=5a. Answer: 2020

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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