Final answer:
Find the parametric equations by using the direction vector (2,1,1) and point (5,1,0). Solve for each coordinate plane intersection by setting the irrelevant variables to zero and computing the corresponding values.
Step-by-step explanation:
To find the parametric equations for the line that passes through the point (5,1,0) and is perpendicular to the plane 2x + y + z = 0, we first need to determine the direction vector of the line. This direction vector is the normal vector to the plane, which is given by the coefficients of x, y, and z in the plane's equation, thus the direction vector is (2,1,1). Using the point (5,1,0) and the direction vector (2,1,1), the parametric equations of the line can be given by x = 5 + 2t, y = 1 + t, and z = 0 + t.
To find the intersection points with the coordinate planes, we set the non-relevant variables to zero:
-
- For the xy-plane (z=0), we already have the point (5, 1, 0).
-
- For the yz-plane (x=0), set x=0 in the parametric equation and solve for t to find y and z.
-
- For the xz-plane (y=0), set y=0 in the parametric equation and solve for t to find x and z.