| 释义 |
vector equation (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 (p − a) · 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(x − x1) + m(y − y1) + n(z − z1) = 0, and the second form becomes the standard linear equation lx + my + nz = constant.
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