C

Step 1: Let's define the vectors. Let vector A have a magnitude of 8.0, pointing along the x-axis, so A = 8.0i.
Step 2: Let vector B be along the x-axis and have a magnitude B. B = Bi.
Step 3: The sum of these two vectors is a new vector C. According to the problem, C lies along the y-axis. Therefore, we can express vector C as C = 2D, where D is the magnitude of vector B.
Step 4: Since the resultant C is vertical, we can infer: C = A + B, which simplifies to (8.0i + Bi) and for this to be purely vertical, B must equal -8.0. Therefore, we have C = 8.0i - 8.0i = 0.
Step 5: But if we have B = 8.0, then by the triangle law of vector addition (Pythagoras theorem): C = \\sqrt{(A^2 + B^2)} = \\sqrt{(8.0^2 + 8.0^2)} = \\sqrt{(64 + 64)} = \\sqrt{128} = 8√2.
Therefore, the magnitude of D is 4√2. According to the problem, the magnitude of the vector C is twice of D hence should be 8√2.
Therefore, the answer is C, which is 8√2.