数学矢量计算,高手进

向量AB = [1, 2, -1]
向量AC = [2, -1, 0]

向量AB与向量AC的叉积

= [2*0 - (-1)*(-1), 2*(-1) - 1*0, 1*(-1) - 2*2]

= [-1, -2, -5]

三角形ABC的面积 = 0.5|AB||AC|sin(角BAC)
【|AB|为向量AB的模，也就是向量AB的长度】

= 0.5*|向量AB与向量AC的叉积|

= 0.5*|[-1,-2,-5]|

= 0.5*[1^2 + 2^2 + 5^2]^(1/2)

= 0.5*[30]^(1/2)

|AD|^2 = 2^2 + 2^2 + 1^2 = 9, |AD| = 3.

|BD|^2 = 1^2 + 0^2 + 0^2 = 1, |BD| = 1.

|CD|^2 = 0^2 + 3^2 + 1^2 = 10, |CD| = (10)^(1/2)

三角形ABC到点D(3,1,1)的距离 = 三角形ABC的3个顶点到点D(3,1,1)的距离的最小值
= |BD| = 1

222