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
To find a × (-b), we first need to determine the vector -b and then compute the cross product. The given vectors are: a = 2i + j (which can be written as 2i + j + 0k) b = -i + 3j + k Step 1: Find the vector -b. To find -b, we multiply each component of b by -1: -b = -(-i + 3j + k) -b = i - 3j - k Step 2: Calculate the cross product a × (-b). We use the determinant formula for the cross product: a × (-b) = i & j & k \\ 2 & 1 & 0 \\ 1 & -3 & -1 Expand the determinant: = i((1)(-1) - (0)(-3)) - j((2)(-1) - (0)(1)) + k((2)(-3) - (1)(1)) = i(-1 - 0) - j(-2 - 0) + k(-6 - 1) = -1i - (-2)j + (-7)k = -i + 2j - 7k Step 3: Compare the result with the given options. The calculated result is -i + 2j - 7k. Let's check the options: (a) -5i + 10j - 3k (b) i + 2j - 7k (c) 5j - 10j + 3k = -5j + 3k (d) None Our calculated vector -i + 2j - 7k does not exactly match option (b) because of the sign of the i component. Since it does not match any of the options (a), (b), or (c), the correct choice is (d). The final answer is (d). That's 2 down. 3 left today — send the next one.