Chapter 13.1, Problem 31E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

At what points does the curve **r**(*t*) = *t* **i** + (2*t* − *t*^{2}) **k** intersect the paraboloid *z* = *x*^{2} + *y*^{2}?

To determine

The points of intersection of curve

Explanation

**Given data:**

The vector equation

**Definition:**

Consider a vector function as
** C** are,

Here,

*x*, *y*, and *z* are parametric equations of ** C**.

From definition, write the parametric equations for vector function

Write the equation of paraboloid.

Substitute *t* for *x*, 0 for *y*, and
*z*,

Hence, there are two possibilities for *t* value. One is

Therefore, values of *t* are 0 and 1

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