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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

If u, v and w are three vectors in 鈩�3, what is wrong with the expression u脳v脳w?

Fill in the blanks to complete each of the following theorem statements:

For 蔚>0,f(x)鈭�(L-蔚,L+蔚)if and only if<蔚.

In Exercises 22鈥�29 compute the indicated quantities when u=(2,1,鈭�3),v=(4,0,1),andw=(鈭�2,6,5)

u脳vandv脳u

Find u+vandu-valso sketch u,v,u+v,u-v

role="math" localid="1649595165778" u=1,-2andv=-3,6

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