   Chapter 11.5, Problem 3E

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 ( 0 , 0 , 0 ) v = 〈 3 , 1 , 5 〉

(a)

To determine

To calculate: Find the parametric equations of a line passing through the point (0,0,0) and is parallel to the vector v=3,1,5.

Explanation

Given:

The line passes through the point (0,0,0) and is parallel to the vector v=3,1,5.

Formula used:

Parametric equations of a line are:

x=x1+at,y=y1+bt

And

z=z1+ct

Calculation:

Let us now to find a set of parametric equations of the line,

For this use the coordinates

x1=0, y1=0

And

z1=0

Also we know the provided point is (0,0,0)

and use the direction numbers

a=3, b=1 and c=5

We also know given parallel vector is v=3,1,5

(b)

To determine

To calculate: Find the symmetric equations of the line which passes through the point (0,0,0) and is parallel to the vector (3,1,5).

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