Answer: Is <-x,-x> Equal to <x,x>?

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In summary, vectors represented as <-x,-x> and <x,x> are equal in two-dimensional space. The order of the components does not affect the vector's properties, and the negative sign in front of the components in <-x,-x> simply indicates a different direction. Vectors with different components can still be equal if they have the same magnitude and direction. The significance of <-x,-x> and <x,x> lies in their representation of the same vector and their usefulness in mathematical and scientific calculations.
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coverband
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Is <-x,-x> = <x,x> !?

Thanks!
 
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That depends on what you mean by <x, x>!

Some people use it to mean a 2 vector. In that case, <-x, -x>= <x, x> only if x= 0. Other wise, <-x, -x>= -<x, x>.

But you may be referring to an inner product in some vector space. If that is so, then <-x, -x>= -< x, -x> = -(-<x, x>)= <x, x> so that is, in fact, true.
 

FAQ: Answer: Is <-x,-x> Equal to <x,x>?

Is <-x,-x> equal to ?

Yes, <-x,-x> and are equal. They both represent the same vector in two-dimensional space, with the same magnitude and direction. The negative sign in front of the components does not change the vector's properties.

Why is the order of the components switched in <-x,-x> compared to ?

The order of the components does not affect the vector's properties. Both <-x,-x> and represent the same vector, but the components are simply written in a different order. This is a common convention in mathematics and science, and it is important to remember that the order of the components does not change the vector's direction or magnitude.

How can <-x,-x> and be equal if they have different signs?

The negative sign in front of the components in <-x,-x> does not change the vector's properties. It simply means that the vector is pointing in the opposite direction compared to , which has positive components. However, both vectors have the same magnitude and direction, making them equal.

Can vectors with different components be equal?

Yes, vectors with different components can still be equal as long as they have the same magnitude and direction. For example, <3,4> and <6,8> may have different components, but they represent the same vector with a magnitude of 5 and direction of 53 degrees from the positive x-axis.

What is the significance of <-x,-x> compared to ?

The significance of <-x,-x> and is that they represent the same vector in two-dimensional space. The negative sign in front of the components in <-x,-x> may indicate that the vector is pointing in the opposite direction compared to , but they still have the same magnitude and direction. This can be useful when working with vectors in mathematical and scientific calculations.

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