Final answer:
To find the vector equation for the line of intersection of two planes, you need to calculate the cross product of their normal vectors.
Step-by-step explanation:
To find the vector equation for the line of intersection of the planes, we need to find the direction vector of the line first. To do this, we can take the cross product of the normal vectors of the two planes. The normal vectors of the planes can be represented as n1 = [5, -4, -4] and n2 = [5, 2, 0]. Taking the cross product of these two vectors, we get the direction vector of the line of intersection: d = n1 x n2 = [8, 20, -30]. So, the vector equation for the line of intersection of the planes is r = [x, y, z] = [x0, y0, z0] + t[8, 20, -30], where [x0, y0, z0] is a point on the line and t is a parameter representing any point on the line.