Answer:
Gradient normal x gradient tangent = -1 is a mathematical expression that relates the normal and tangent vectors of a curve in three-dimensional space. The gradient of a scalar function is a vector that points in the direction of the greatest rate of increase of the function. The normal vector is perpendicular to the surface defined by the function, and the tangent vector is a vector that lies on the surface and points in the direction of the curve.
In mathematics, the cross product of two vectors is a vector that is orthogonal to both vectors, and the magnitude of the cross product is equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between them. In this case, the normal and tangent vectors of a curve form an orthogonal basis, meaning that they are perpendicular to each other. The expression gradient normal x gradient tangent = -1 says that the magnitude of the cross product of the normal and tangent vectors is equal to -1. This means that the normal and tangent vectors form a right-handed coordinate system, where the cross product is negative because the normal vector points in the opposite direction to the positive z-axis.