Final answer:
To find the unique point on the axis that is on both planes, set up a system of equations using the equations of the two planes. To find a unit vector with a positive first coordinate that is parallel to both planes, take the cross product of the normal vectors of the planes and divide by the length.
Step-by-step explanation:
In order to find the unique point on the axis that is on both planes, we need to find the intersection point of the two planes. To do this, we can set up a system of equations using the equations of the two planes. Once we find the intersection point, we can determine the coordinates of the unique point on the axis that is on both planes.
To find a unit vector with a positive first coordinate that is parallel to both planes, we can take the cross product of the normal vectors of the two planes. The resulting cross product will give us a vector that is perpendicular to both planes. Dividing this vector by its length will give us a unit vector with a positive first coordinate.