   Chapter 11.5, Problem 108E

Chapter
Section
Textbook Problem

# Finding Parametric EquationsFind a set of parametric equations for the line passing through the point ( 1 , 0 , 2 ) that is parallel to the plane given by x + y + z = 5 and perpendicular to the line x = t , y = 1 + t , z = 1 + t .

To determine

To calculate: Find the parametric equation of line passing through the point (1,0,2) and is parallel to the plane given by, x+y+z=5.

Explanation

Given:

Line is passing through the point (1,0,2)

Plane given by,

x+y+z=5.

Line is,

x=t,y=1+t,z=1+t.

Formula used:

Parametric equation of a line is given by,

x=x1+at,y=y1+bt,z=z1+ct.

Calculation:

Normal vector n of the provided plane will be perpendicular to the required line as

the required line is parallel to the provided plane,

Equation of plane:

x+y+z=5.

Hence direction numbers will be the coefficients of x,y,z in the equation of plane.

Hence we have, n=1,1,1

Again as, the required line is perpendicular to the provided line,

this shows the required line is perpendicular to the parallel vector v of the provided line.

provided line is,

x=t,y=1+t,z=1+t

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 