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
Step 1: Find the position vector of M. M is the midpoint of XY. The position vector of M, OM, is given by: OM = (1)/(2)(OX + OY) Substitute the given vectors OX = -4i + 6j and OY = 12i - 6j: OM = (1)/(2)((-4i + 6j) + (12i - 6j)) OM = (1)/(2)((-4+12)i + (6-6)j) OM = (1)/(2)(8i + 0j) OM = 4i + 0j Step 2: Find the position vector of N. Given that ON:NY = 1:2, N divides the line segment OY in the ratio 1:2. Therefore, the position vector of N, ON, is: ON = (1)/(1+2)OY = (1)/(3)OY Substitute OY = 12i - 6j: ON = (1)/(3)(12i - 6j) ON = ((1)/(3) × 12)i - ((1)/(3) × 6)j ON = 4i - 2j Step 3: Find the vector NM. The vector NM is found by subtracting the position vector of N from the position vector of M: NM = OM - ON Substitute the calculated OM and ON: NM = (4i + 0j) - (4i - 2j) NM = (4-4)i + (0 - (-2))j NM = 0i + 2j Step 4: Calculate the magnitude of NM. The magnitude of a vector ai + bj is given by sqrt(a^2 + b^2). |NM| = sqrt(0^2 + 2^2) |NM| = sqrt(0 + 4) |NM| = sqrt(4) |NM| = 2 Correct to 1 decimal place, the magnitude is 2.0. The magnitude of NM is 2.0 units. Send me the next one 📸