MHB Another equation of another line

[ineedhelpnow]

Please help, how do I do this?
Find the parametric and symmetric equation for a line through (1,-1,1) and parallel to $x+2= \frac{1}{2}y=z-3$

So confused

 

[Prove It]

Please help, how do I do this?
Find the parametric and symmetric equation for a line through (1,-1,1) and parallel to $x+2= \frac{1}{2}y=z-3$

So confused

Parallel lines have the same direction vectors.

Can you get a direction vector for $\displaystyle \begin{align*} x + 2 = \frac{1}{2}y = z - 3 \end{align*}$?

 

[ineedhelpnow]

That's what I'm stuck on.at first I though it would be v=(-2,2,3) but then I came to the conclusion that it was wrong so I am stuck again.

 

[Prove It]

That's what I'm stuck on.at first I though it would be v=(-2,2,3) but then I came to the conclusion that it was wrong so I am stuck again.

You need to get better at the problem solving strategy of thinking in reverse. How would you go from a vector form of a line to the symmetric form?

Start by writing out the x, y, z components separately to get the parametric equations.

Solve for t in each equation.

Realise since they are all equal to t, they are equal to each other.

Now how do you think you can go in reverse to get back to the vector equation?

 

[ineedhelpnow]

i figured it out :)