   Chapter 11.5, Problem 6E

Chapter
Section
Textbook Problem

# Finding Parametric and Symmetric Equations In 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.)Point Parallel to ( − 3 , 0 , 2 ) v = 6 j + 3 k

(a)

To determine

To calculation: Find the parametric equations of a line passing through the point (3,0,2) and is parallel to the vector v=6j+3k.

Explanation

Given:

The line passes through the point (3,0,2) and is parallel to the vector v=6j+3k.

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=3, y1=0

and z1=2

Also we know the given point is (3,0,2) and

and use the direction numbers

a=0, b=6 and c=3

Now the parallel vector is provided in the standard form, that is v=6j+3k.

Also the, component form of the provided vector is v=0,6,3 as there is no i in the standard form of vector v

(b)

To determine

To calculate: Find the symmetric equations of the line which passes through the point (3,0,2) and is parallel to the vector v=6j+3k.

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