   Chapter 11.5, Problem 7E

Chapter
Section
Textbook Problem

# Finding Parametric and Symmetric EquationsIn Exercises 7–12, find sets of (a) parametric equations and (b) symmetric equations of the line that passes through the given point and is parallel to the given vector or line. (For each line, write the direction numbers as integers.)PointParallel to ( 1 , 0 , 1 ) x = 3 + 3 t , y = 5 − 2 t , z = − 7 + t

(a)

To determine

To calculate: Line passing through the available point and is in parallel to the provided vector /line x=3+3t,y=52t and z=7+t, determine the parametric equation of line.

Explanation

Given:

Line is parallel to the below mentioned vector and passes through the point (1,0,1)

x=3+3t,y=52t And z=7+t.

Formula used:

Line is defined by following parametric equations

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

Calculation:

Since, line to be found must be parallel to the line x=3+3t,y=52t and z=7+t, hence it must also be parallel to the vector in parallel to the given line 3,2,1

So, in order to find out set of parametric equations use the coordinates x1=1,y1=0 and z1=1 as the given point is (1,0,1).

Parametric equations of a line can be represented as;

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

Here, a,b and c are the direction numbers of the parallel vector of the line

(b)

To determine

To calculate: Line passing through the available point and is in parallel to the provided vector /line x=3+3t,y=52t and z=7+t, determine the symmetric equation of line.

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