Describe in your own words what a negative vector is
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Steven G
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It is a vector which has magnitude and direction.
HallsofIvy
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In a "linearly ordered set" such as the real numbers, rational number, integers, .... you can identify one element a "0", elements to one side as "positive", elements on the other side as "negative". But vectors are not "linearly ordered" so there is no way to declare one set as "negative" and another as "positive". Of course, given a vector you multiply that vector by the scalar -1 and get the "negative" of the original vector. In that sense the "negative" of <a, b> is <-a, -b>.
Dr.Peterson
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Since "negative" as an adjective means "less than zero", and vectors can't be compared as greater or less, there is no such thing as a negative vector. So my word would be "nonexistent". Note that you can't say that <2,5> is positive and <-2,-5> is negative; that would leave <2,-5> out of the picture.
The word "negative" can also be used as a noun: the negative of 3 is -3. In that sense, you can talk about the negative of a vector; the negative of <2,-5> is <-2,5>. But that's not what your question is asking about.
The word "negative" can also be used as a noun: the negative of 3 is -3. In that sense, you can talk about the negative of a vector; the negative of <2,-5> is <-2,5>. But that's not what your question is asking about.