# Finding Two Vectors from Vector Sum / Difference

Finding Two Vectors from Given Linear Combination

## Homework Statement

If v + w = (5,1) and v - w = (1,5), compute and draw v and w.

v + w = (5,1)
v - w = (1,5)

## The Attempt at a Solution

I understand how to find the sum of two vectors, but I'm confused on how to find the vectors from a sum / difference. My first attempt was to draw the v + w vector and v - w vector and try to visualize the original two vectors, v and w. However, I couldn't come up with anything productive.

If it matters, I'm going through MIT OCW 18.06 w/ Introduction to Linear Algebra (Strang) and this is question 3 from problem set 1.1. Its been a few years since I took LA or any vector math and I'm trying to regain lost knowledge.

Any guidance would be greatly appreciated.

Last edited:

SteamKing
Staff Emeritus
Homework Helper
"I understand how to find the sum of two vectors, but I'm confused on how to find the vectors from a sum / difference."

What happens if you add the two equations together in Section 2 of the OP? What happens if you subtract them?

1 person
"I understand how to find the sum of two vectors, but I'm confused on how to find the vectors from a sum / difference."

What happens if you add the two equations together in Section 2 of the OP? What happens if you subtract them?
Adding them would give 2v = (6,6), which would make vector v = (3,3). Subtracting them would give 2w = (4,-4), which would make vector w = (2,-2).

Wow, wish I would've seen that on my own. Thanks for the "nudge" in the correct direction.