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Chapter 10: Q .3. (page 833)

What is a linear equation in three variables? Give an example. What is the graph of a linear equation in three variables?

Short Answer

Expert verified

Ax+By+Cz=DwhereA,B,C,Dconstants;2x+4y-7z=2;plane.

Step by step solution

01

Step 1:Given information

A linear equation in three variables

02

Step 2:Explaination

A linear equation is an algebraic equation in which each term is either a constant or the product of constant and a variable of exponent one.

An equation of the formAx+By+Cz=Dis called a linear equation in three variables, where A,B,CDare scalars.

An Example of an equation in three variables is 2x+4y-7z=2

Each linear equation which has three variables determines a plane in three - dimensional space.

Thus the graph of a linear equation in three variables represents a plane.

Hence, the answer is,

Ax+By+Cz=DwhereA,B,C,Dconstants;2x+4y-7z=2;plane.

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Most popular questions from this chapter

In Exercises 30–35 compute the indicated quantities when

u=(−3,1,−4),v=(2,0,5),andw=(1,3,13)

u×vandv×u

If u, v and w are three vectors in ℝ3, which of the following products make sense and which do not?

localid="1649346164463" (a)u·(v·w)(b)u·(v×w)(c)u×(v·w)(d)u×(v×w)

In Exercises 30–35 compute the indicated quantities when u=(−3,1,−4),v=(2,0,5),andw=(1,3,13)

Find the area of the parallelogram determined by the vectors u and v.

In Exercises 24-27, find compuv,projuv and the component of v orthogonal tou.

role="math" localid="1649693816584" u=3,1,-2,v=-6,-2,4

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

u=-5,1,3,v=-3,2,7
See all solutions

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