Minimum distance between two straight lines Calculator tool

straight line passes through A(a1,b1,c1) parallel to vector V1(p1,q1,r1)
point A(,,)
vector V1(,,)
straight line passes through B(a2,b2,c2) parallel to vector V2(p2,q2,r2)
point B(,,)
vector V2(,,)
The shortest distance between two straight lines (d)

First converts the straight line Equation to a symmetric form, receiving its vector n1= (a1,b1,c1),n2=(a2,b2,c2).

Take two vectors Cross multiplication to receive their common perpendicular vector N= (x,y,z), and select point A,B(arbitrarily) on two straight lines. receive vector AB, vector AB in the direction of vector N projection is the distance between the straight line of two different faces (is the shortest distance), know how to find?

d=| vector N* vector AB|/| vector N| (the above is the product of two vector numbers, and the below is Mold seeking), set the intersection point as C,D, and put it into the symmetric formula of male vertical line N. And since the two points C and D respectively satisfy the straight line Equation at the beginning, it is good to solve the two continued equations of C (or D) separately.

formulas :