How do you simplify vectors?
1)AB + BC + CD
2) BC - FE - BA + DE - DC
Calculus - Steve, Tuesday, September 22, 2015 at 11:39pm
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
Calculus - Anonymous, Tuesday, September 22, 2015 at 11:57pm
I need an explanation on how to do it. I just started learning this and it doesn't make sense to me.
Line them up on a number line.
for 2)
BC + EF + AB + DE + CD
AB + BC + CD = AD
DE + EF = DF
so
AD + DF
but AD + DF = AF
so in the end
AF
Well, simplifying vectors is like organizing a clown car - you want to make sure everyone gets in the right order and no one gets left behind.
For the first expression, AB + BC + CD, you can combine AB and BC to get AC. Then, you can combine AC and CD to get AD. So, the simplified form is AD.
Now, for the second expression, BC - FE - BA + DE - DC, it's a little trickier. Remember, when adding or subtracting vectors, order matters. It's like trying to juggle with bowling pins - you need to keep your eye on the right pins.
Let's rearrange the terms to line up the ends in order. First, BC and DC have the same starting point, so you can combine them to get BD. Then, we have BA, which has the same starting point as BD. But, since it's subtracted, you can think of it as BA in the opposite direction, or -AB. So, BD - AB = BD + (-AB) = BD - AB.
Next, we have -FE and DE. Since they have different starting points, we can't directly combine them. But, if we think of -FE as EF (same magnitude but opposite direction), then we can combine EF and DE to get DF.
Finally, we have BD - AB + DF. BD and AB don't have the same starting points, so we can't combine them directly. But, if we think of BD as DB (opposite direction), then we can combine DB and AB to get AD.
So, the simplified form of BC - FE - BA + DE - DC is AD.
I hope that explanation made things a little clearer for you. Just remember, simplifying vectors is like juggling, but with a mathematical twist!
To simplify vectors, you can add or subtract vectors that have the same starting and ending points. Here's how you can simplify the given vectors:
1) AB + BC + CD:
Since AB and BC have the same starting and ending points (B), you can simplify them by adding them together: AB + BC = AC.
Now, you have AC + CD. Since AC and CD have the same starting and ending points (C), you can simplify them by adding them together: AC + CD = AD.
Therefore, the simplified form of AB + BC + CD is AD.
2) BC - FE - BA + DE - DC:
First, let's rearrange the terms so that the endings of the vectors line up in order:
BC - BA - FE + DE - DC
Now, let's simplify each pair of vectors that have the same starting and ending points:
BC - BA = BC + (-BA) = BC - BA (No simplification possible since BA is opposite to AB)
FE - DE = FE + (-DE) = FE - DE (No simplification possible since DE is opposite to ED)
Now, you have BC - BA - FE + DE - DC.
Since BA and BC have the same starting and ending points (B), you can simplify them by subtracting them: BC - BA = AB.
Now, you have AB - FE + DE - DC.
Since AB and DC have the same starting and ending points (D and B are connected), you can simplify them by adding them together: AB - FE + DE - DC = AE - FE.
Finally, the simplified form of BC - FE - BA + DE - DC is AE - FE.
I hope this explanation helps you understand how to simplify vectors! Let me know if you have any further questions.
To simplify vectors, we need to combine like terms and rearrange the terms if necessary.
Let's go through each example step by step:
1) AB + BC + CD:
To simplify this vector, we can combine AB and BC. Since AB + BC = AC, we can replace AB + BC with AC.
Now the expression becomes AC + CD.
Since AC and CD do not have any like terms or matching ends to add or subtract, we cannot simplify this further. Therefore, the simplified vector is AC + CD.
2) BC - FE - BA + DE - DC:
To simplify this vector, we need to rearrange the terms in a way that we can combine like terms. Let's reorganize the terms with matching ends:
BC - BA - DC + DE - FE
Now, we can combine BC and BA, as well as DC and DE:
(BC - BA) - DC + DE - FE
BC - BA simplifies to C, and DC + DE simplifies to DE.
Thus, the expression becomes:
C - DE - FE
Again, there are no further like terms or matching ends to add or subtract, so the simplified vector is C - DE - FE.
Keep in mind that simplifying vectors involves combining like terms and rearranging terms when necessary. It is essential to pay attention to the directions and matching ends of the vectors to properly simplify them.