   Chapter 12.1, Problem 91E

Chapter
Section
Textbook Problem

# True or False? In Exercises 91–94, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If f, g, and h are first-degree polynomial functions, then the curve given by x = f(t), y = g(t) and z = h(t) is a line.

To determine

Whether the provided statement is true or false “If f,g and h are first degree polynomial function, then the curve by x=f(t),y=g(t), and z=h(t) is a line.”

Explanation

Given:

If f,g and h are first degree polynomial function, then the curve by x=f(t),y=g(t), and z=h(t) is a line.

If f,g and h are first degree polynomial function, then the curve by x=f(t),y=g(t) and z=h(t) is,

r(t)=f(t)i+g(t)j+h(t)k

The vector function r(t) is a linear function because f,g and h are first degree polynomial function. Since, the linear vector function represents a line equation.

Thus, the provided statement is true.

For- example- let the vector function, r(t)=ti+(2t+1)j+tk

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