Final answer:
The magnitude of the vector that has an x-component of 3 units and makes a 30° angle with the horizontal is approximately 3.46 units, none of the given options match this result.
Step-by-step explanation:
The question asks for the magnitude of a vector that makes an angle of 30° with the horizontal and has an x-component equal to 3 units. To find this, we use the definition of the cosine function in trigonometry, which is the adjacent side (x-component) over the hypotenuse (magnitude of the vector). Because we know the cosine of 30° is √3/2 and we have the adjacent side (x-component), we can set up the equation √3/2 = 3 / magnitude. To find the magnitude, we rearrange the equation to magnitude = 3 / (√3/2). The magnitude of the vector is therefore 2√3, which simplifies to approximately 3.46 units.