Vector Subtraction: Is it Commutative?

• odolwa99
In summary, the conversation discusses whether or not it is valid to say that \vec{am}=-\frac{1}{2}\vec{a}+\vec{c} when considering \vec{am}=\frac{1}{2}\vec{ao}+\vec{c}. The conclusion is that this statement is valid because vector addition is commutative.
odolwa99

Homework Statement

Just a quick question. In the attached image, I can say $\vec{am}=\vec{c}-\frac{1}{2}\vec{a}$. Although subtraction is not commutative, can I also say (relative strictly to vectors) that $\vec{am}=-\frac{1}{2}\vec{a}+\vec{c}$, considering $\vec{am}=\frac{1}{2}\vec{ao}+\vec{c}$?

Many thanks.

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odolwa99 said:

Homework Statement

Just a quick question. In the attached image, I can say $\vec{am}=\vec{c}-\frac{1}{2}\vec{a}$. Although subtraction is not commutative, can I also say (relative strictly to vectors) that $\vec{am}=-\frac{1}{2}\vec{a}+\vec{c}$, considering $\vec{am}=\frac{1}{2}\vec{ao}+\vec{c}$?

Many thanks.
Subtraction isn't commutative, as you noted, but addition is, and that's really what you're doing. a - b = a + (-b), which is the same as -b + a.

odolwa99 said:

Homework Statement

Just a quick question. In the attached image, I can say $\vec{am}=\vec{c}-\frac{1}{2}\vec{a}$. Although subtraction is not commutative, can I also say (relative strictly to vectors) that $\vec{am}=-\frac{1}{2}\vec{a}+\vec{c}$, considering $\vec{am}=\frac{1}{2}\vec{ao}+\vec{c}$?

Many thanks.

Saying that $\ \vec{am}=\vec{c}-\frac{1}{2}\vec{a}\$ is essentially the same as saying $\ \vec{am}=-\frac{1}{2}\vec{a}+\vec{c}\,,\$ because $\ \vec{c}-\frac{1}{2}\vec{a}=\vec{c}+ \left(-\frac{1}{2}\vec{a}\right)\$ and vector addition is commutative.

Great. Thank you very much.

What is vector subtraction?

Vector subtraction is the process of combining two or more vectors to find their difference. It involves finding the vector that, when added to the second vector, results in the first vector.

Is vector subtraction commutative?

No, vector subtraction is not commutative. This means that the order in which the vectors are subtracted changes the result. In other words, A - B is not the same as B - A.

How is vector subtraction calculated?

To subtract vectors, we use the head-to-tail method. This involves placing the tail of the second vector at the head of the first vector, and then drawing a new vector from the tail of the first vector to the head of the second vector. This new vector represents the result of the subtraction.

Can vector subtraction be applied to any type of vector?

Yes, vector subtraction can be applied to any type of vector, whether they are 2-dimensional or 3-dimensional, and whether they represent physical quantities or mathematical entities.

What is the significance of vector subtraction in science?

Vector subtraction plays a crucial role in many scientific fields, such as physics, engineering, and mathematics. It allows us to calculate the difference between two vectors, which is essential in understanding the relationships between physical quantities and in solving complex mathematical problems.

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