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.
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Another one Ðƴŋâmïč̣ — let's solve it. We are given two vectors: a = 2i - 3j + k b = -3i + j - 2k We need to find the magnitude of 2a - 3b. Step 1: Calculate 2a. Multiply each component of a by 2: 2a = 2(2i - 3j + k) 2a = 4i - 6j + 2k Step 2: Calculate 3b. Multiply each component of b by 3: 3b = 3(-3i + j - 2k) 3b = -9i + 3j - 6k Step 3: Calculate 2a - 3b. Subtract the components of 3b from the corresponding components of 2a: 2a - 3b = (4i - 6j + 2k) - (-9i + 3j - 6k) 2a - 3b = (4 - (-9))i + (-6 - 3)j + (2 - (-6))k 2a - 3b = (4 + 9)i + (-6 - 3)j + (2 + 6)k 2a - 3b = 13i - 9j + 8k Step 4: Find the magnitude of 2a - 3b. For a vector V = xi + yj + zk, its magnitude is given by |V| = sqrt(x^2 + y^2 + z^2). Let V = 2a - 3b = 13i - 9j + 8k. |2a - 3b| = sqrt((13)^2 + (-9)^2 + (8)^2) |2a - 3b| = sqrt(169 + 81 + 64) |2a - 3b| = sqrt(314) The magnitude of 2a - 3b is sqrt(314). Drop the next question.