This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Alright Justify — let's do this. To find a unit vector perpendicular to the plane containing two vectors, we first calculate their cross product, and then divide the resulting vector by its magnitude. Given vectors: P = 3i - 2j + 4k Q = i + j - 2k Step 1: Calculate the cross product N = P × Q. N = i & j & k \\ 3 & -2 & 4 \\ 1 & 1 & -2 N = i((-2)(-2) - (4)(1)) - j((3)(-2) - (4)(1)) + k((3)(1) - (-2)(1)) N = i(4 - 4) - j(-6 - 4) + k(3 - (-2)) N = 0i - j(-10) + k(5) N = 10j + 5k Step 2: Calculate the magnitude of N. |N| = sqrt((0)^2 + (10)^2 + (5)^2) |N| = sqrt(0 + 100 + 25) |N| = sqrt(125) |N| = sqrt(25 × 5) |N| = 5sqrt(5) Step 3: Find the unit vector n. A unit vector perpendicular to the plane can point in two opposite directions, so we include ±. n = ± N|N| = ± 10j + 5k5sqrt(5) n = ± ( (10)/(5sqrt(5))j + (5)/(5sqrt(5))k ) n = ± ( (2)/(sqrt(5))j + (1)/(sqrt(5))k ) n = (B) ± (1)/(sqrt(5))(2j + k) Send me the next one 📸