Question

Consider the planes 1x+5y+5z=1 and 1x+5z=0
Answer the following:
A) Find the unique point P on the y-axis which is on both planes.
B) Find the unit vector u with positive first coordinate that is parallel to both planes.
C) Use parts (A) and (B) to find a vector equation for the line of intersection of the two planes, r(t) =?

Answer 1

A. The intersection point is y= 1/5 with points (0,1/1,5).
B. The cross product of normal vectors is the vector parallel to both planes. The product of (1,5,5) and  (1,0,5) is (25, 0, -5)
C. The corresponding coordinate of the answers from A and B.