Final answer:
No. The sum of two vectors is the vector beginning from the first vector's origin and ending at the second vector's tip, as per the head-to-tail method. The resultant vector combines both direction and magnitude, which is determined by vector addition, not arithmetic sum of magnitudes.
Step-by-step explanation:
The sum of two vectors is indeed the vector that starts from the origin of the first vector and ends at the tip of the second vector when using the head-to-tail method. This method entails placing the tail of the second vector at the head of the first vector, and then drawing a new vector (the resultant) from the origin of the first vector to the tip of the second vector. The resultant vector represents the combined effect of the two individual vectors.
Remember, vector quantities have both magnitude and direction. When we talk about the sum of two vectors, what's important is the direction and length of the resultant vector, not just the arithmetic sum of the magnitudes. For instance, if Ax = 3 m east, Ay= 4 m north, the resultant vector A will have a magnitude that follows the Pythagorean theorem, resulting in a 5 m north-east direction, not simply 7 m (3 m + 4 m).
To find this resultant analytically, you would add up the horizontal components and the vertical components separately, Ax + Ay = A. This scalar addition provides the necessary components to express the resultant vector.