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: Identify the given vectors. Let the three vectors be v_1, v_2, and v_3. v_1 = i + 4j + 2k v_2 = 3i - 3j - 2k v_3 = -2i + 2j + 6k Step 2: Calculate the sum of the vectors. Let S be the sum of the vectors. S = v_1 + v_2 + v_3 S = (i + 4j + 2k) + (3i - 3j - 2k) + (-2i + 2j + 6k) Combine the i, j, and k components: S = (1+3-2)i + (4-3+2)j + (2-2+6)k S = 2i + 3j + 6k Step 3: Calculate the modulus (magnitude) of the sum vector S. The modulus of a vector xi + yj + zk is given by sqrt(x^2 + y^2 + z^2). ||S|| = sqrt((2)^2 + (3)^2 + (6)^2) ||S|| = sqrt(4 + 9 + 36) ||S|| = sqrt(49) ||S|| = 7 Step 4: Compare the result with the given options. The calculated modulus is 7. This matches option (b) for question 8. The final answer is (b) 7. What's next?