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 the angle that the vector r = sqrt(3)i + j makes with the x-axis, we can use the components of the vector. Step 1: Identify the x and y components of the vector. The given vector is r = sqrt(3)i + j. Here, the x-component is x = sqrt(3) and the y-component is y = 1. Step 2: Use the tangent function to find the angle. The angle that a vector (x, y) makes with the positive x-axis is given by the formula: () = (y)/(x) Substitute the values of x and y: () = (1)/(sqrt(3)) Step 3: Calculate the angle . We need to find the angle whose tangent is (1)/(sqrt(3)). We know that (30^) = (1)/(sqrt(3)). Since both x and y components are positive, the vector lies in the first quadrant, so the angle is 30^. = ((1)/(sqrt(3))) = 30^ The angle is 30^. Comparing this with the given options, option A is 30^. The final answer is A. 30^. That's 2 down. 3 left today — send the next one.