Find the linear equation which is parallel to the intersection of two planes x-4z = 3 and 2x-y-5z = 1 and passes through the point (- 3,2,5) Do you want to ask whether the lower intersection line can be obtained by subtracting the two plane equations directly? That is, the intersection line equation is X-Y-Z = - 2?

Find the linear equation which is parallel to the intersection of two planes x-4z = 3 and 2x-y-5z = 1 and passes through the point (- 3,2,5) Do you want to ask whether the lower intersection line can be obtained by subtracting the two plane equations directly? That is, the intersection line equation is X-Y-Z = - 2?

There are three methods. One is to take two points on the intersection line. For example, take z = 0, x = 3, y = 5 to get a (3,5,0), then take z = 1, x = 7, y = 8 to get B (7,8,1), so the direction vector of the intersection line is ab = (4,3,1), so the direction vector of the intersection line is ab = (4,3,1)