Final answer:
The component form of vector 2QS, where Q = (3,4) and S = (2, -8), is (2, 24) and its magnitude is 24.08 (rounded to two decimal places).
Step-by-step explanation:
The question involves finding the component form and the magnitude of the vector 2QS, where Q = (3,4) and S = (2, -8). To find the component form, we first find the vector QS by subtracting the coordinates of S from the coordinates of Q, giving us QS = Q - S = (3 - 2, 4 - (-8)) = (1, 12). Then, to find 2QS, we multiply each component of QS by 2, resulting in 2QS = (2 × 1, 2 × 12) = (2, 24).
To find the magnitude of the vector 2QS, we use the Pythagorean theorem, where the magnitude is the square root of the sum of the squares of its components. So, the magnitude of 2QS is |2QS| = √(2² + 24²) = √(4 + 576) = √580 = 24.08 (rounded to two decimal places).