Study the information provided below on two vectors: Then calculate the magnitudes of $\vec{a}+\vec{b}$ by the method of vector resolution. Assume that the magnitude of each vector is 100 units

Step 1 ：Given two vectors with magnitudes of 100 units each.

Step 2 ：The components of the first vector, \(\vec{a}\), are \(a_x = 100.0\) and \(a_y = 0.0\).

Step 3 ：The components of the second vector, \(\vec{b}\), are \(b_x = 6.123233995736766e-15\) and \(b_y = 100.0\).

Step 4 ：When the vectors are added together, the resulting vector will have components that are the sum of the components of the original vectors. Thus, \(res_x = 100.0\) and \(res_y = 100.0\).

Step 5 ：The magnitude of the resulting vector can be calculated using the Pythagorean theorem, which gives a magnitude of approximately 141.4213562373095 units.

Step 6 ：This makes sense because the two original vectors were at right angles to each other and had the same magnitude. The resulting vector is the hypotenuse of a right triangle with sides of 100 units, so its length is the square root of the sum of the squares of the sides, which is approximately 141.42 units.

Step 7 ：Final Answer: The magnitude of \(\vec{a}+\vec{b}\) is approximately \(\boxed{141.42}\) units.