vector equation

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(of a plane)

Given a plane in 3-dimensional space, let a be the position vector of a point A in the plane, and n a normal vector to the plane. Then the plane consists of all points P whose position vector p satisfies (pa). n=0. This is a vector equation of the plane. It may also be written p. n=constant. By supposing that p has components x, y, z, that a has components x1, y1, z1, and that n has components l, m, n, the first form of the equation becomes l(xx1)+m(yy1)+n(zz1)=0, and the second form becomes the standard linear equation lx+my+nz=constant.

Subjects: Mathematics.

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