Chapter 13.1, Problem 42E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Find a vector function that represents the curve of intersection of the two surfaces.

**42.** The cylinder *x*^{2:} + *y*^{2} = 4 and the surface *z* = *xy*

To determine

**To find**: the vector function of the curve that intersects two surfaces.

Explanation

**Given data:**

The equations of cylinder as

**Definition:**

Consider parametric equations as

Write the expression for vector function in terms of parametric equations.

Here,

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

The equation of cylinder is
*z*-plane is
*x* as
*y* as

Substitute
*x* and
*y* in cylinder equation

The right hand side (RHS) is equal to the left hand side (LHS)

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