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So I am watching Khan Academy Linear Algebra series and I keep getting confused on direction of vector that is sum or difference of vectors. For example for three dimensional vectors Sal is talking about plane and two vectors that point from the origin to the plane position and form third vector that lies on this plane. So $x_0 - x_1$ he draws as a vector from $x_1$ to $x_0$. I am confused why it is the case, while $x_0 + x_1$ is a vector from $x_1$ to $x_0$.
Thanks!
You should treat vector addition as adding vectors end-to-end. When you add a vector to another, you could (in this case - mind you!) draw the first vector $x_{0}$ and then start drawing $x_{1}$ on its end point. To deduct a vector, add its negative.
You'll have to pay close attention to the placement and orientation of the vectors.
If $\vec{x}$ and $\vec{y}$ are two vectors, and we place the start of $\vec{y}$ at the end of $\vec{x}$, then $\vec{x}+\vec{y}$ is the vector from the start of $\vec{x}$ to the end of $\vec{y}$.
If we place the start of both $\vec{x}$ and $\vec{y}$ at the same point, then $\vec{x}-\vec{y}$ is the vector from the end of $\vec{y}$ to the end of $\vec{x}$.
