# Homework Help - Finding a Vector, and values of s and t, when given an equality

There is not an example problem in my textbook that I can reference (I have said this on two other questions so far, but it's the truth. The example problems and solutions manual contain physics / engineering examples rather than abstract examples).

For this one, I did not know how to begin. Normally I would give the work I had done, even if it is incorrect.

For what values of t and so does the equality <4-2t, 2s-4t >= < s+4t, 3+2t>. Find t and s. At these values of t and s, find the resulting vector.

Can anyone point me in the correct direction or give me an idea on how to solve this?

Set the $x$-components equal to each other and the $y$-components equal to each other.
Two vectors are equal if and only if they are identical: the first component of each should be equal, the second component of each should be equal. So for the vectors $\langle 4-2t, 2s-4t\rangle$ and $\langle s+4t, 3+2t\rangle$ to be equal, you must have $4-2t = s+4t$ (first components equal) and $2s-4t = 3+2t$ (second components equal). This is a system of two equations in two unknowns; solve them to find (all) value(s) of $s$ and $t$ that make the equality true. Then plug the values to get the "resulting vector"(s).