converting between vector lines in R3 and parametric form

[jay1793]

x − a/ d = y − b /e = z − c/ f .
Convert this line (at least the vectors [x, y, z] T satisfying these equalities) to parametric form.

 

[Steven G]

I have a question for you. Do you want to be involved in solving this question or do you just want us to solve it for you? This will help know how to proceed with your post. BTW, did you read the guidelines for this forum?

 

[Dr.Peterson]

x − a/ d = y − b /e = z − c/ f .
Convert this line (at least the vectors [x, y, z] T satisfying these equalities) to parametric form.

Presumably what you meant was

(x − a)/ d = (y − b) /e = (z − c)/ f​

Do you see the importance of the parentheses for clear communication?

Now you need to tell us what you know about the subject, what you have tried, and where you are stuck, so that we can have some idea of what specific help you need.

Do you know what "parametric form" means? Have you seen examples?

 

[pka]

x − a/ d = y − b /e = z − c/ f .
Convert this line (at least the vectors [x, y, z] T satisfying these equalities) to parametric form.

Please, please use grouping symbols, It should be (x − a)/ d =( y − b) /e = (z − c)/ f .
To convert to parametric: \(\ell(t)=\left<a+d\cdot t,<b+e\cdot t,c+f\cdot t\right>\)
\(\ell(t)=\left\{ \begin{array}{l}a+d\cdot t\\b+e\cdot t\\c+f\cdot t\end{array} \right.\)

 

[Dr.Peterson]

To convert your form to parametric form (in the most natural way), you just have to give a name to the value of the three equal ratios:

(x − a)/ d = (y − b) /e = (z − c)/ f = t​

Then just solve for each of the coordinates x, y, and z, in terms of the parameter t.