使向量垂直于另一个向量的公式是什么?

问题描述

要得到一个垂直于矢量A的平面上的三维矢量B的公式是什么?

What is a formula to get a three dimensional vector B lying on the plane perpendicular to a vector A?

也就是说，给定一个向量A，公式f(angle，modulus)是什么，它给出一个垂直于A的向量，具有所述模数并旋转一个角度?

That is, given a vector A, what is a formula f(angle,modulus) which gives a vector that is perpendicular to A, with said modulus and rotated through an angle?

推荐答案

如果两个向量垂直，则它们的点积为零.

If the two vectors are perpendicular then their dot product is zero.

所以:v1(x1, y1, z1), v2(x2, y2, z2).

=> x1 * x2 + y1 * y2 + z1 * z2 = 0

您知道(x1, y1, z1).放置任意x2和y2，您将收到相应的z2:

You know (x1, y1, z1). Put arbitrary x2 andy2 and you will receive the corresponding z2:

z1 * z2 = -x1 * x2 - y1 * y2
=> z2 = (-x1 * x2 - y1 * y2) / z1

请注意z1是否为0.那你在飞机上.

Be aware if z1 is 0. Then you are in the plane.

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