What is th difference between orthogonal and perpindicular?

Question

wikipedia says there the same, but is there situations (in math) where they can mean slightly different things?

Answer 1

Perpendicular refers only to two objects.

Orthogonal refers to a set of objects, that any two of them must be perpendicular.

Answer 2

"Perpendicular" tends to refer to what we think of visually by perpendicular: two things (lines, planes, etc.) meeting at a right angle. It turns out that when two 2-D vectors are perpendicular, they have certain numerical properties, such was what happens to their dot product, etc. But you can take these same numerical properties and expand it for vectors that might have 3, 4, 5, 6 or even more components. This is also very helpful when using matrix manipulation in linear algebra.

However, at that point calling them "perpendicular" might not make much visual sense, because at that point you're doing math on things that can't necessarily be graphically represented as simple lines, so there aren't any "right angles" necessarily happening. That's why "orthogonal" is a helpful term here.

Answer 3

Literally they are the same, but orthogonal is the more general term. We can have two planes, curves, surfaces and even dimensions which are orthogonal to each other. This means that a vector which uniquely defines the set (normal for a plane) is perpendicular to a similar vector of another set.

Answer 4

This is the name for their dot product's sum. If the i and j componenets dot product is 0 then they are orthagonal. If they are perpindicular their dot product is 0 so wikipedia was correct. You know this is in refernce to vector study? Don't mean to insult you if you know already.