   Chapter 12.1, Problem 94E

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.The vector-valued function r(t) = t2i + t sin tj + t cos t k lies on the paraboloid x = y2 + z2.

To determine

Whether the provided statement is true or false “the vector-valued function r(t)=t2i+tsintj+tcostk lies on the paraboloid x=y2+z2.”

Explanation

Given:

The vector value function r(t)=t2i+tsintj+tcostk lies on the paraboloid x=y2+z2.

The vector value function,

r(t)=t2i+tsintj+tcostk,

Compare the above equation with the standard equation, r(t)=f(t)i+g(t)j+h(t)k. Here, f(t)=t2,g(t)=tsint and h(t)=tcost.

Now, calculate the value of {g(t)}2+{h(t)}2,

{g(t)}2+{h<

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