: You are given the vectors u = (2, 1, 1, 2) and v = (3, 2, −1, 2). Find the values of t such that u · (u + tv) = 16

Question



Answer 1

u•(u + tv) = (2,1,1,2)•((2,1,1,2) + t(3,2,-1,2)) = (2,1,1,2)•(2 + 3t,1 + 2t, 1 - t, 2 + 2t) = 4 + 6t + 1 + 2t + 1 - t + 4 + 4t = 16; 10 + 11t = 16; t = 6/11