Question

DETAILS LARLINALG8 5.R.022. Determine all vectors that are orthogonal to u. (If the system has an infinite number of solutions, express V, V, and v, in terms of the parameters s and t.) u = (1, -2, 1) V-

Answer 1

Let be orthogonal to (1,-2,1)

That means, u.v = 0

$(1,-2,1).(v_1,v_2,v_3) = 0 \implies v_1 - 2v_2 + v_3 = 0$

Thus,

Thus, there are infinitely many solutions. If we let and , then

Thus, all vectors that are orthogonal to u is of the form where $s,t \in \mathbb{R}$