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
Hey Attitude, good to see you again. To find the unit vector in the direction of the sum of the given vectors, we first need to find the sum of the vectors and then divide it by its magnitude. The given vectors are: v_1 = i + 4j + 2k v_2 = 3i - 3j - 2k v_3 = -2i + 2j + 6k Step 1: Find the sum of the vectors. Let R be the resultant vector. R = v_1 + v_2 + v_3 R = (i + 4j + 2k) + (3i - 3j - 2k) + (-2i + 2j + 6k) Combine the corresponding components: R = (1+3-2)i + (4-3+2)j + (2-2+6)k R = 2i + 3j + 6k Step 2: Calculate the magnitude of the resultant vector R. The magnitude of a vector ai + bj + ck is sqrt(a^2 + b^2 + c^2). |R| = sqrt((2)^2 + (3)^2 + (6)^2) |R| = sqrt(4 + 9 + 36) |R| = sqrt(49) |R| = 7 Step 3: Find the unit vector in the direction of R. The unit vector R is given by R|R|. R = 2i + 3j + 6k7 R = (2)/(7)i + (3)/(7)j + (6)/(7)k Comparing this result with the given options, it matches option (d). The final answer is (d). Send me the next one 📸