Is it assumed that dot product of 0 means perpendicular? (2 Viewers)

[robkay]

If I prove the dot product of two vectors is zero, is it then assumed that the vectors are perpendicular or is an extra line of work required to prove why it means theyre perpendicular?

 

[Nav123]

If I prove the dot product of two vectors is zero, is it then assumed that the vectors are perpendicular or is an extra line of work required to prove why it means theyre perpendicular?

Yes its enough, if you really want to you can add a line saying:



but this is not neccesary.

 

[Luukas.2]

It is NOT true to say that, just because the dot product of two vectors a and b is zero, it follows that a and b are perpendicular. The correct inference is that EITHER a and b are perpendicular OR at least one of the vectors a or b is the zero vector.

Formally, once you have shown that a . b = 0, you can infer that a and b are perpendicular provided neither |a| nor |b| is zero.

So, a . b = 0 implies a and b are perpendicular so long as a and b are both non-zero vectors.