The length of the x-component of a vector can be determined by projecting the vector onto the x-axis. In this case, we need to find the horizontal component of the given vector, Vectory.
To do this, we look at the position of the vector on the x-axis. From the given options, we can see that the x-component of Vectory is not directly provided.
To determine the x-component, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the x-component as one of the sides of a right triangle, and the magnitude (length) of the vector as the hypotenuse.
Let's assume that the magnitude of the vector is 5 units (this value is not provided in the question, but we'll use it for illustration purposes). If the vector is plotted as shown, we can see that the x-component is 3 units and the y-component is 4 units.
Using the Pythagorean theorem, we can calculate the magnitude (length) of the vector:
magnitude = (x-component 2 + y-component 2)
magnitude = (3^2 + 4^2)
magnitude = (9 + 16)
magnitude = /25
magnitude = 5
Now, we can determine the length of the x-component by using the magnitude of the vector and the length of the y-component:
x-component = (magnitude ^2 - y-component^2)
x-component = (5^2 - 4^2)
x-component = V(25 - 16)
x-component = 19
x-component = 3
Therefore, the length of the x-component of Vectory is 3.
None of the provided options match the correct answer of 3.