How to think of $\vec{u}-\vec{v}$

Question

Assume I have two vectors, $\vec{u}$ and $\vec{v}$. I know that I can think of their sum via Triangle or Parallelogram Law, but I'm having trouble knowing which way the vector would point depending on if it was $\vec{u}-\vec{v}$ or if it was $\vec{v}-\vec{u}$. Is there an easy way to remember which way the arrow would point?

Answer 1

Instead of memorizing the direction, you could try thinking $$\vec{u} = (\vec{u}-\vec{v}) + \vec{v},$$ i.e., $\vec{u}-\vec{v}$ would point to the direction from the tip of $\vec{v}$ to the tip of $\vec{u}$.

Answer 2

$\vec{u} -\vec{v} = \vec{u} + (-\vec{v}) $ now the direction of $-\vec{v}$ is just $180^0$ opposite to that of direction of $\vec{v}. $ Now it is just addition of two vectors so you can determine direction

Answer 3

You can think about $\vec{u}-\vec{v}$ as a translation of the origin from $\vec{0}$ to $\vec{v}$. In this case $\vec{v}$ becomes the new origin and thus has the tail of the new vector.

Answer 4

Understand and remember $Displacement=End-Start$. So in subtraction of vectors the result starts from tip of vector that is subtracted.

Answer 5

Remember that $\vec{u}-\vec{0}=\vec{u}$ is the vector from the origin to $\vec{u}$. This reminds me that $\vec{u}-\vec{v}$ is in the direction from $\vec{v}$ to $\vec{u}$.