Line-plane intersection
Three-dimensional geometry and vector algebra · Mathematics
Study notes
Q: Where does r = (1,2,3)+t(1,1,1) meet x + y + z = 12? Is r = (0,0,0)+t(1,−1,0) parallel to it? Substitute: (1+t)+(2+t)+(3+t) = 12 → 6+3t = 12 → t = 2. Point (3,4,5). Second: d·n = (1,−1,0)·(1,1,1) = 0: parallel (origin not on plane, so no intersection).