- #1
transgalactic
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i have vector "a"
why a*a=1??
it make no sense
the formula says |a|*|a|*cos0=a^2 (not 1)
why a*a=1??
it make no sense
the formula says |a|*|a|*cos0=a^2 (not 1)
Scalar multiplication of two equal vectors
- Thread starter transgalactic
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In summary, the conversation discusses the confusion of the formula |a|*|a|*cos0=a^2 not equating to 1, as well as the professor's statement about multiplying a vector by itself resulting in 1. The conversation concludes with the suggestion that the professor may have been referring to a unit vector, which represents a single unit with a direction of a certain axis, but does not necessarily have a length of 1.
- #2
tiny-tim
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Hi transgalactic! 
But cos0 = 1,
so that means |a|*|a| = a^2, which is correct.
Where does your a*a=1 come from?
transgalactic said:
But cos0 = 1,
so that means |a|*|a| = a^2, which is correct.
Where does your a*a=1 come from?
- #3
transgalactic
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from my professor in physics :(
- #4
tiny-tim
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transgalactic said:
Well, what was the context, then?
What else was he/she talking about at the time?
Unit vectors? Basis vectors? General vectors? Hilbert spaces?
- #5
transgalactic
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he just stated that if we multiply scalarly a vector(in general) by itself
we will get 1
we will get 1
- #6
tiny-tim
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transgalactic said:
hmm … that's obviously rubbish …
i suppose he must have been thinking of applying that to some specific equation that he didn't actaully mention.
- #7
transgalactic
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ill try to confront him with this problem
- #8
HallsofIvy
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Are you sure he didn't say a unit vector?
- #9
transgalactic
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unit vector represents a single unit with the direction of a certain axes
i think you are correct
why their multiplication equals 1?
nobody said their length is 1
only that its the smallest unit of length with a direction
??
i think you are correct
why their multiplication equals 1?
nobody said their length is 1
only that its the smallest unit of length with a direction
??
1. What is scalar multiplication of two equal vectors?
Scalar multiplication of two equal vectors is the process of multiplying each component of one vector by a scalar value and then adding the resulting products to the corresponding components of the other vector. This results in a new vector with the same direction as the original vectors, but with a magnitude that is the product of the scalar value and the magnitude of the original vectors.
2. Why is scalar multiplication useful in vector operations?
Scalar multiplication is useful in vector operations because it allows us to scale the magnitude of a vector while preserving its direction. This is particularly useful in physics and engineering, where vectors are often used to represent physical quantities such as force and velocity.
3. How is scalar multiplication different from vector addition?
Scalar multiplication and vector addition are two different operations. Scalar multiplication involves multiplying a vector by a scalar value, while vector addition involves adding two or more vectors together. Scalar multiplication results in a new vector, while vector addition results in a sum of multiple vectors.
4. Can scalar multiplication of two equal vectors result in a zero vector?
Yes, scalar multiplication of two equal vectors can result in a zero vector if the scalar value is equal to zero. This is because multiplying each component of a vector by zero will result in a vector with all components equal to zero, which is the definition of a zero vector.
5. Is scalar multiplication commutative for two equal vectors?
Yes, scalar multiplication is commutative for two equal vectors. This means that if we multiply a vector by a scalar value and then multiply the same vector by a different scalar value, the result will be the same as if we had multiplied the two scalar values together and then multiplied the vector by the product.
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