I'm quite stumped on the following problem: Consider the planes 4x + 1y + 1z = 1 and 4x + 1z = 0. (A) Find the unique point P on the y-axis which is on both planes. (_, _, __)
(B) Find a unit vector u with positive first coordinate that is parallel to both planes __I + __J + _K
(C) Use the vectors found in parts (A) and (B) to find a vector equation for the line of intersection of the two planes r(t) = __I + __J + _K
Work thus far: I've figured out (A) is (0,1,0) Now, I know that the dot product of <4,1,1> and u will = 0, as well as the dot product between <4,0,1> and u... I'm quite stumped. Can anyone help me out by giving me hints? I'd prefer that the entire solution isn't given yet, so I can work through it. I'll respond as quickly as I can.