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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9.6 Equations of Lines and Planes

Focus on plane normal and normal vector.

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.

01Equations of lines in spaceWorked steps · five questions02Equations of planesWorked steps · five questions03Plane through three pointsWorked steps · five questions
Lesson brief and rules

9.6 Equations of Lines and Planes

A plane with normal ⟨a,b,ca,b,c⟩ has form ax+ax+ by ++ cz =d=d.

Worked example 11
01 / Give a normal vector to 3x+5y+4z=73x+5y+4z=7.
02 / The coefficients of x,y,zx,y,z form a normal vector.
03 / Answer: ⟨3,5,43,5,4⟩
Worked example 2 · Normal vector

Find a normal vector to 4x+6y+8z=14x+6y+8z=1.

The x,y,zx,y,z coefficients form a normal vector. Answer: ⟨4,6,84,6,8⟩

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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