To determine if the line g intersects the plane e orthogonally, we need to check if the direction vector of the line is perpendicular to the normal vector of the plane. If the dot product of the direction vector of the line and the normal vector of the plane is zero, then the line intersects the plane orthogonally. If the dot product is not zero, then the line does not intersect the plane orthogonally. **

A square in the complex plane always has two solutions because the square root of a complex number has two possible values. This is due to the fact that complex numbers have both a real and an imaginary component, and the square root of a complex number can be expressed in two different forms. Therefore, when taking the square root of a complex number, there are always two possible solutions, each corresponding to a different combination of the real and imaginary parts of the original number. **

To reflect a plane on the plane x1x3, you would first find the equation of the plane you want to reflect. Then, you would substitute x2 with -x2 in the equation to reflect it across the x1x3 plane. This means changing the sign of the coefficient of x2 in the equation of the plane. The resulting equation will be the reflection of the original plane across the x1x3 plane. **

To reflect a plane across the plane x1x3, you can first find the equation of the mirror plane x1x3. Then, for each point on the original plane, you can find its reflection across the mirror plane by using the formula for reflecting a point across a plane. This involves finding the perpendicular distance from the point to the mirror plane and then using that distance to find the reflected point. By applying this process to all points on the original plane, you can obtain the reflected plane across the x1x3 plane. **

To determine the coordinate equation of the plane E, we need to know a point on the plane and the normal vector to the plane. Let's say the point on the plane is P(x1, y1, z1) and the normal vector is N(a, b, c). Then the coordinate equation of the plane E is given by ax + by + cz = d, where d = ax1 + by1 + cz1. This equation represents all the points (x, y, z) that lie on the plane E. **

An infinite number of solutions is a characteristic of a plane in the context of linear equations. When solving a system of linear equations, a plane can have an infinite number of solutions if the equations are dependent, meaning they represent the same line or plane. In this case, the solutions form a continuous set of points that lie on the line or plane. Therefore, an infinite number of solutions is indeed a part of the plane in the context of linear equations. **

To determine a parallel plane to a given plane, you can use the normal vector of the given plane. If the normal vector of the given plane is (a, b, c), then the parallel plane will have the same normal vector. You can then use this normal vector to find the equation of the parallel plane. If the given plane has the equation Ax + By + Cz + D = 0, then the parallel plane will have the equation Ax + By + Cz + K = 0, where K is a constant. This will ensure that the two planes are parallel to each other. **

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