I What does vector subtraction for two non-perpendicular vectors look like?

[homeworkhelpls]

TL;DR Summary

confused

vector subtraction of ppl is simple but i cant visualise the subtraction please help

 

[Vanadium 50]

If a -b = a + (-b) for scalars, what do you think it would be for vectors?

 

[Herman Trivilino]

Can you visualize the addition of vectors?

 

[kuruman]

 

[homeworkhelpls]

If a -b = a + (-b) for scalars, what do you think it would be for vectors?

same thing?

 

[PeroK]

same thing?

What @Vanadium 50 meant is that subtraction is actually addition of the (additive) inverse. In basic arithmetic, subtraction is seen as a separate arithmetic operation. But, as you progress in mathematics you'll see that there is only really addition.

 

[MidgetDwarf]

In general A+ (-B ) = A - B. We can think of this visually as drawing the tail of a vector from the tip of B to the tip of A. This will be A - B. Assuming A and B originate at the same point.

Here is another way. As shown in Kuraman's diagram:

Multiplying by a negative 1, changes the direction of a vector, but keeps it magnitude the same. Then follow the parallelogram rule for addition of vectors. This is what's occurring in the diagram.

 

[kuruman]

To @homeworkhelpls :
Since you asked specifically about the difference between two vectors, here is a recipe for subtracting vectors graphically which summarizes what has already been said.

• Put the vectors tail to tail and connect the tips with a line segment. This is the magnitude of the difference, $|\mathbf{A}-\mathbf{B}|.$
• Put an arrowhead at the end of the segment touching the tip of the vector that comes first in the difference that you want to represent. This will convert the segment from a magnitude to a vector, i.e. define the direction of the difference.

Note that when you start where the tails are together and move in the direction of the arrows:

• in (1) if you go to the left, you reach directly the tip of $\mathbf{A}$; if you go to the right, you trace the path $\mathbf{B}+(\mathbf{A-B})=\mathbf{A}$, same place.
• in (2) if you go to the right, you reach directly the tip of $\mathbf{B}$; if you go to the left you trace the path $\mathbf{A}+(\mathbf{B-A})=\mathbf{B}$, same place.