N 1=( 1, 0, -4), n2 = (2,-1, -5)-N 1, n2 is the normal vector of two planes and their intersection (the direction vector of). (space geometry theorem: the perpendicular of the plane is perpendicular to all the straight lines in the plane. )

From vector multiplication, we can know that the vertical vector of two vectors can be obtained by the cross product of two vectors. Therefore, the direction vector S of a straight line can be obtained by the cross product of the known normal vector n 1 and n2. That is, s0=n 1 across n2.

( 1,0,-4) × (2,- 1,-5) = (| (0,4) (- 1,-5) |, | (-4, 1) (-5,

=(0-4,-8+5,- 1-0)=(-4,-3,- 1)

According to analytic geometry theorem, two straight lines are parallel and their direction vector components are proportional. When the scale value is 1, the two direction vectors are equal. So s=s0. As for the point where l crosses M0, it should be a known condition of the topic, and there should be no need to explain it!