Orthogonal Lines Math

In elementary geometry orthogonal is the same as perpendicular. Two vectors v and w of the real plane r 2 or the real space r 3 are orthogonal iff their dot product v w 0. In geometry the word orthogonal simply means at right angles.

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We also sometimes say they are normal to each other.

Orthogonal lines math. 2 g g 2 f f c c. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. In mathematics orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms. In other words the orthogonal trajectories are another family of curves in which each curve is perpendicular to the curves in original family.

Two elements u and v of a vector space with bilinear form b are orthogonal when b 0. Two lines or planes are orthogonal if they are at right angles 90 to each other. Depending on the bilinear form the vector space may contain nonzero self orthogonal vectors. If two circles are cut orthogonally then it must satisfy the following condition.

The orthogonal trajectories are the curves that are perpendicular to the family everywhere. By extension orthogonality is also used to refer to the separation of specific features of a system. Orthogonal circles two circles are said to be orthogonal circles if the tangent at their point of intersection are at right angles. In the image below the lines ab and pq are orthogonal because they are at right angles to each other.

In the case of function spaces families of orthogonal functions are used to form a basis.