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 unit vector u in the same direction as vector v, we use the formula u = (v)/(||v||), where ||v|| is the magnitude of vector v. Step 1: Identify the given vector. The given vector is v = 4 \\ -2 \\ 1 . Step 2: Calculate the magnitude of vector v. The magnitude of a vector x \\ y \\ z is given by ||v|| = sqrt(x^2 + y^2 + z^2). ||v|| = sqrt(4^2 + (-2)^2 + 1^2) ||v|| = sqrt(16 + 4 + 1) ||v|| = sqrt(21) Step 3: Calculate the unit vector u. u = (1)/(||v||) v u = (1)/(sqrt(21)) 4 \\ -2 \\ 1 Step 4: Compare with the given options. The calculated unit vector matches option a. The final answer is a. (1)/(sqrt(21)) 4 \\ -2 \\ 1 . That's 2 down. 3 left today — send the next one.