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Answer :
To determine the magnitude of vector A - 2B, subtract twice vector B from A and calculate the square root of the sum of the squares of the resulting vector's components, yielding the magnitude \\[ \\sqrt{449} \\] meters.
To find the magnitude of the vector A - 2B, first subtract the vector 2B from vector A. Vector A is given as (3.0x, 4.0y) meters and vector B as (5.0x, 12.0y) meters. We start by multiplying vector B by 2, resulting in a new vector (10.0x, 24.0y) meters. Subtracting this from vector A, we obtain a resulting vector (-7.0x, -20.0y) meters. To find the magnitude, we apply the formula for the magnitude of a vector, which is the square root of the sum of the squares of its components. The calculation will be \\[ \\sqrt{(-7.0)^2 + (-20.0)^2} \\].
The magnitude of the vector A - 2B is therefore \\[ \\sqrt{49 + 400} = \\sqrt{449} \\] meters. This is the direct answer to how to find the magnitude of a vector when dealing with subtracting and scaling other vectors.
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