How Do You Calculate the Second Vector in a Vector Displacement Problem?

[singingblonde]

Homework Statement

A man pushing a mop across a floor causes the mop to undergo two displacements. The first has a magnitude of 150 cm and makes an angle of 120 degrees with the positive x axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35 degrees to the positive x axis. Find the magnitude and direction of the second displacement (second vector)

Homework Equations

Vector Component Addition

The Attempt at a Solution

I realize that somehow, we know the resultant vector and one of the vectors and need to solve for the second vector. Because nothing is known about the second vector, I don't know how to go about that. I've been working on this problem all day and truly need some help.

 

[CompuChip]

Hi singingblonde.

Suppose for a moment that the problem was reversed: the two vectors were given (for example: 150 cm with an angle of 120 degrees with the x-axis, and 140 cm at an angle of 35 degrees to the x-axis) and you were asked to calculate the resultant vector. Would you know how to solve that?