Determine the magnitude of $A B$ given $A(6,1)$ and $B(2,2)$. 3 $4 i$ $\sqrt{17}$ $\sqrt{3}$

Step 1 ：Given points A(6,1) and B(2,2), we need to find the magnitude of AB.

Step 2 ：The magnitude of a vector AB, given two points A(x1, y1) and B(x2, y2), can be calculated using the distance formula which is derived from the Pythagorean theorem. The distance d between two points A and B is given by the formula: \(d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\)

Step 3 ：Substitute the given values into the formula: \(d = \sqrt{(2 - 6)^2 + (2 - 1)^2}\)

Step 4 ：Solve the equation to get the decimal value of the magnitude of AB, which is approximately 4.123105625617661.

Step 5 ：The options provided in the question are in the form of square roots. Therefore, we need to simplify the decimal number to a square root form.

Step 6 ：The simplified magnitude of AB is still approximately 4.123105625617661. This is closest to the square root of 17, which is approximately 4.123105625617661.

Step 7 ：Therefore, the magnitude of AB is \(\sqrt{17}\)

Step 8 ：Final Answer: \(\boxed{\sqrt{17}}\)