Final answer:
To determine the parametric equations for the line of intersection between two planes, we typically find a common point on both planes and calculate the direction vector by taking the cross product of the normal vectors of the planes. However, the provided answer options do not seem to correspond to the intersection of the correctly stated planes.
Step-by-step explanation:
The student is asking for the parametric equations of the line of intersection between two planes given by the equations x+y+z=1 and x=2y+24. To find this, we need to find a point of intersection and the direction vector for the line. First, these two planes are parallel to the y-axis since their normal vectors are perpendicular to the y-axis (the vectors are [1, 1, 1] and [2, 0, 0] respectively). The planes intersect when their x and z values are the same, so by setting x equal to 2y+24 in the first equation, we can solve for y and z. To find the direction vector, we take the cross product of the normals of the two planes. This process will give the direction vector (dx, dy, dz).
Assuming the student is provided with more information to eliminate the incorrect choices, we find that none of the options given directly match the parameters described by the intersection of the two original planes. However, if we assume there has been a typo and the second equation was meant to be x=2y+24 (as it is not currently a plane), we would find parameters for the intersection. Therefore, it is important to verify the correct equations of the planes before calculating the line of intersection.