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Reference.org
Tangential and normal components
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, given a <a href="/facts/Vector_(geometric)/bCLrdksy">vector</a> at a point on a <a href="/facts/Curve/xBQ0pTBW">curve</a>, that vector can be decomposed uniquely as a sum of two vectors, one <a href="/facts/Tangent/sF0jH3EI">tangent</a> to the curve, called the tangential component of the vector, and another one <a href="/facts/Perpendicular/u0k8xqx4">perpendicular</a> to the curve, called the normal component of the vector. Similarly, a vector at a point on a <a href="/facts/Surface_(topology)/jK1b1KIG">surface</a> can be broken down the same way. </p><p>More generally, given a <a href="/facts/Submanifold/zcUy3Enk">submanifold</a> <i>N</i> of a <a href="/facts/Manifold/rXPERJtu">manifold</a> <i>M</i>, and a vector in the <a href="/facts/Tangent_space/crvpbSeG">tangent space</a> to <i>M</i> at a point of <i>N</i>, it can be decomposed into the component tangent to <i>N</i> and the component normal to <i>N</i>. </p>