# A silly question about equations....

• ViolentCorpse
In summary, the confusion arises when trying to express the relationship between two equal but opposite vectors in mathematical form. The correct way to express this mathematically is A + B = 0, not A - B = 0. This is because the vectors have opposite directions, but equal magnitudes. In the example of circuit analysis, the equation is Vi + V0 = 0, not Vi - V0 = 0, as the voltage across the resistor should be treated as negative. The key is to plug in the quantities before changing the signs during addition.
ViolentCorpse
Hi,

I'm not sure if this belongs in the Maths section, so I'm sorry if I've made a mistake.

I'm having trouble understanding the meaning of the most basic sorts of equations.
For example, if we have two exactly equal but opposite force vectors A and B acting on a body, then by Newton's law the algebraic sum of these forces must equal zero. If you ask me to write these words in maths, I would write it like this:
A - B = 0,
which implies that
A=B

But that goes against my intuition. I mean to say that, if you ask me to immediately express the relationship between two vectors that are equal yet opposite, in mathematical form, I would write it like this:

A= -B

I'm confused which one of these equations expresses the relationship correctly. Please help me understand what is the correct way of expressing this mathematically, and why.

Thank you!

ViolentCorpse said:
Hi,

I'm not sure if this belongs in the Maths section, so I'm sorry if I've made a mistake.

I'm having trouble understanding the meaning of the most basic sorts of equations.
For example, if we have two exactly equal but opposite force vectors A and B acting on a body, then by Newton's law the algebraic sum of these forces must equal zero. If you ask me to write these words in maths, I would write it like this:
A - B = 0,
which implies that
A=B

But that goes against my intuition. I mean to say that, if you ask me to immediately express the relationship between two vectors that are equal yet opposite, in mathematical form, I would write it like this:

A= -B

I'm confused which one of these equations expresses the relationship correctly. Please help me understand what is the correct way of expressing this mathematically, and why.

Thank you!

The sum of the forces is equal to zero implies A + B = 0, not A - B = 0.

A and B would be force vectors, which have magnitude and direction. If A and B are equal and opposite, their magnitudes will be the same, and their directions will be opposite. Make sense?

ViolentCorpse
ViolentCorpse said:
A=B
That the equation for the magnitudes.

ViolentCorpse said:
A= -B
That the equation for the vectors.

ViolentCorpse
ViolentCorpse said:
For example, if we have two exactly equal but opposite force vectors A and B acting on a body, then by Newton's law the algebraic sum of these forces must equal zero.
They can't be "exactly equal" if their directions are different. As already pointed out, their magnitudes can be equal even though the vectors themselves are different (and therefore unequal).

ViolentCorpse
A.T. said:
That the equation for the magnitudes.
But I found that equation out using Newton's law, which I think handles vectors?

The same problem has confused me in circuit analysis when applying kirchhoffs voltage law. Suppose we have a battery of volts Vi connected to a resistor whose voltage is Vo. By KVL, the equation would be

Vi-Vo=0
Vi=Vo

Although Vi and Vo have opposite polarities. Again, I think Vi= -Vo, would be the correct expression of the relationship. Is the KVL equation only about magnitudes like Newton's?

ViolentCorpse said:
But I found that equation out using Newton's law, which I think handles vectors?
Sure, but you're misunderstanding what the vectors represent. If they are oppositely directed, with equal magnitudes, then their vector sum will be the zero vector. For example, suppose ##\vec{A}## = <1,1> and ##\vec{B}## = <-1, -1>. The first vector points in the NE direction, and the second points in the SW direction, so their directions are directly opposite one another. Both vectors have magnitudes of ##\sqrt{2}##.

##\vec{A} + \vec{B}## = <1, 1> + <-1, -1> = <0, 0>.
ViolentCorpse said:
The same problem has confused me in circuit analysis when applying kirchhoffs voltage law. Suppose we have a battery of volts Vi connected to a resistor whose voltage is Vo. By KVL, the equation would be

Vi-Vo=0
Vi=Vo

Although Vi and Vo have opposite polarities. Again, I think Vi= -Vo, would be the correct expression of the relationship. Is the KVL equation only about magnitudes like Newton's?
The business about the opposite polarities is where the signs come in. If you take the voltage potential across the battery to be positive, then the voltage drop across the resistor should be treated as negative. Assuming Vi = 6V, then V0 would be -6V. The equation is Vi + V0 = 0.

ViolentCorpse
So basically, I'm making the mistake of changing the sign + to - during the addition of symbols that represent the quantity, without plugging in the quantity first, right?

Thanks a lot guys! :)

## What is an equation?

An equation is a mathematical statement that shows the relationship between two or more quantities. It consists of an equal sign, variables, and numbers or symbols.

## Why are equations important?

Equations are important because they allow us to solve problems and make predictions using mathematical concepts. They are used in various fields such as physics, chemistry, engineering, and economics.

## What is the difference between an equation and a formula?

An equation is a specific type of mathematical statement that shows the relationship between variables, while a formula is a general mathematical rule or principle that can be used to solve a variety of problems.

## How do you solve an equation?

To solve an equation, you need to isolate the variable on one side of the equal sign and simplify the other side. This involves using various algebraic operations such as addition, subtraction, multiplication, and division.

## Can equations be used in the real world?

Yes, equations are used in the real world to solve problems and make predictions. For example, the laws of motion in physics can be represented by equations, and businesses use equations to calculate profits and losses.

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