Question

Give a vector parametric equation for the line through the point (5,2,5) that is parallel to the line <-3-t,3-5t,2t-2>:

Answer 1

how far have you gotten with this?

Answer 2

no where.

Answer 3

the equation you are given is in the form\[\vec r(t)=\vec P_1+\vec vt\]where \(\vec v\) is the vector that is parallel to the line, and \(\vec P_1\) is the position vector for the point
can you identify \(\vec v\) in this case?

Answer 4

Would it be the negative reciprocal of <-3-t,3-5t,2t-2>?

Answer 5

no, notice how we can write the equation like so:\[\langle-3-t,3-5t,2t-2\rangle=\langle-3,3,-2\rangle+t\langle -1,-5,2\rangle\]

Answer 6

compare that to\[\vec r(t)=\vec P_1+\vec vt\]and you should be able to identify \(\vec P_1\) and \(\vec v\)