Vectors & Determinants Questions & Answers

Let a = i + 2j + 2k. Vectors u and v satisfy u × v = a, v × a = u, and u · v = 0. Let u = xi + yj + zk, where x, y, z ∈ &bold;R&bold;, and let t ∈ &bold;R&bold; satisfy: tx + y + z = 0, x + ty + z = 0, x + y + tz = 0. Match List-I with List-II: List-I (P) |v|2 (Q) If x = 2, then z2 (R) If x = 2, then (y + z)2 (S) If x = √2, then t + 1 List-II (1) 1 (2) 1 (3) 4 (4) 2 (5) 3