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**Orthogonal polynomials are perpendicular??**

hi..

So as the title suggests, i have a query regarding orthogonal polynomials.

What is the problem in defining orthogonality of polynomials as the tangent at a particular x of two polynomials are perpendicular to each other, for each x? This simply follows the perpendicular vectors or planes etc.

What was the need of defining orthogonality as inner product of the two polynomials are zero? Inner product is given as

∫w(x)*f1(x)*f2(x)=0 over a define interval (that determines the limit)

where w(x)is called the weight function, w(x)>0 for all x in the given interval.

can someone explain what this inner product begin zero mean geometrically, if possible?

(please pardon me for asking a geometrical explanation on this Abstract & linear maths forum.)