Two possibilities for its x component?

[alexoftennis]

Homework Statement

You are given a vector in the xy plane that has a magnitude of 85.0 units and a y component of -50.0 units.?

The two possibilities for its x component are + and - 68.74.

Assuming the x component is known to be positive, specify the vector which, if you add it to the original one would give a resultant vector that is 70.0 units long and points entirely in the -x direction.

Magnitude = ?
Direction = ? degree

Homework Equations

The Attempt at a Solution

I found the first part of the problem which was "What are the two possibilities for its x component?" But I can't get the right answer for the second part. I'm doing this online so I know if I get it wrong or right.

 

[tiny-tim]

Welcome to PF!

Hi alexoftennis! Welcome to PF!

You are given a vector in the xy plane that has a magnitude of 85.0 units and a y component of -50.0 units.?
…
Assuming the x component is known to be positive, specify the vector which, if you add it to the original one would give a resultant vector that is 70.0 units long and points entirely in the -x direction.

From the first part, you have a vector (x,y), which you need to subtract from the vector (-70,0).

Just use vector (component-wise) addition. ​