How do you simplify vectors?
1)AB + BC + CD
2) BC - FE - BA + DE - DC
AB+BC = AC
so, AB+BC+CD = AD
BC-DC = BC+CD = BD
See if you can use that idea to rearrange +/- terms so the ends line up in order
I need an explanation on how to do it. I just started learning this and it doesn't make sense to me.
you need to review addition of vectors. AB starts at A and ends at B
BC starts at B and ends at C
So, AB+BC starts at A and ends at C.
ABC form a triangle.
google will provide lots of illustrations and examples of vector addition
To simplify vectors, you need to combine any like terms by adding or subtracting them accordingly. Like terms are vectors that have the same magnitude and direction.
Let's simplify the given expressions:
1) AB + BC + CD:
To simplify this expression, we add the vectors with the same initial and final point:
AB + BC = AC
Then, we add the remaining vector:
AC + CD = AD
So, the simplified expression is AD.
2) BC - FE - BA + DE - DC:
Again, we will combine the vectors with the same initial and final point:
BC - BA = AC
Next, we combine the remaining vectors:
-AC - FE + DE - DC
Now, we need to group the like terms together and simplify:
(-AC + DE) + (-FE - DC)
Combining the first group of like terms:
-AC + DE = AD
Combining the second group of like terms:
-FE - DC = -EF - CD
Final simplified expression:
AD - EF - CD