Final answer:
To find the x and y components, equate the coefficients of x in the given plane equations and rearrange the equation to isolate y.
Step-by-step explanation:
In a rectangular (Cartesian) xy-coordinate system, the x-component of a vector represents its projection onto the x-axis, while the y-component represents its projection onto the y-axis. We can find the x and y components by comparing the given plane equations.
Given the planes:
1) 4x + 5y + 5z = 1
2) 4x + 5z = 0
To find the x-component, we can equate the coefficients of x in both equations:
4x + 5y + 5z = 1 (equation 1)
4x + 5z = 0 (equation 2)
Subtracting equation 2 from equation 1, we get:
5y + 5z = 1
Now rearrange the equation to isolate y:
5y = 1 - 5z
y = (1 - 5z)/5
Therefore, the x-component is 0 and the y-component is (1 - 5z)/5.