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File: vector-division.png ( 12.35 KB , 1478x540 , 1726609814969.png )

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  No. 964
>>969
Any reason not to teach the algebra of Euclidean vectors like this? This would come after multiplication of vectors by scalars but before the scalar product of two vectors, and the target audience is students at the level of typical high school juniors or seniors.
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  No. 969 >>970
>>964
unpedagogical trash. Introduce the structures mathematicians actually care about. "Keeping it simple" is just a way to stay uneducated. Renminder, there's no royal road to math mastery
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  No. 970
>>969
Finally somebody gets it
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  No. 971 >>972
>Introduce the structures mathematicians actually care about.
Which would include the structure in OP.
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  No. 972 >>973
>>971
Ah yes, my favorite structure of the map taking two vectors from a normed vector space, the second of which is nonzero, and outputting the unique scalar by which one is to scale the second such that it is closest to the first one. Certainly we should teach examples of this before the notion of a vector space is introduced, giving it a designated name.
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  No. 973 >>974
>>972
rather important in inner product spaces bro
albeit the scaled vector moreso than the scalar itself
the remainder is important too
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  No. 974
>>973
Yeah, it's an important example of orthogonal projections

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