Final answer:
The magnitude of |2u|, where u is the vector from x(-4,6) to Y(8,3), is approximately 24.74.
Step-by-step explanation:
To answer the question of what |2u| is, where u is the vector defined by u = vec (xY), with points x(-4,6) and Y(8,3), we need to first find the vector u by subtracting the coordinates of point x from point Y, then take its magnitude and finally calculate the magnitude after the vector has been scaled by a factor of 2.
The vector u is found by calculating the differences between the corresponding coordinates of points Y and x, which gives us u = Y - x = (8 - (-4), 3 - 6) = (12, -3).
The magnitude of u is calculated using the Pythagorean theorem, |u| = \sqrt{12^2 + (-3)^2} = \sqrt{144 + 9} = \sqrt{153} \approx 12.37.
Since we are interested in |2u|, which is the magnitude of the vector u scaled by a factor of 2, we simply multiply the magnitude of u by 2. This gives us |2u| = 2 * |u| = 2 * 12.37 \approx 24.74.