Final answer:
To find a unit vector with positive first coordinate that is parallel to both planes, you need to determine the direction of the normal vectors of the planes, take their cross product, then normalize the resulting vector.
Step-by-step explanation:
To find a unit vector with positive first coordinate that is parallel to both planes, we need to determine the direction of the normal vector of the planes. Let's assume the equations of the planes are given as follows:
Plane 1: ax + by + cz = d
Plane 2: dx + ey + fz = g
From the given information, we can determine the normal vectors of the planes using the coefficients of x, y, and z. The normal vectors of the planes are (-a, -b, -c) and (-d, -e, -f).
To find the unit vector that is parallel to both planes, we can take the cross product of these two normal vectors and then normalize the resulting vector.
Let's denote the cross product as N = (-a, -b, -c) x (-d, -e, -f).
The unit vector in the same direction as N is given by U = N / |N|, where |N| represents the magnitude of N.