How can tangent vector and normal vector be derived? The tangent vector is t = [1, y '(x), Z' (x)] The normal vector is n = (f'x, f'y, f'z) How are the above two points derived? I only know that the slope k of the point slope is the derivative of Y over X, The tangent vector of a curve, the normal vector of a surface. Why is one tangent vector and the other normal vector?

How can tangent vector and normal vector be derived? The tangent vector is t = [1, y '(x), Z' (x)] The normal vector is n = (f'x, f'y, f'z) How are the above two points derived? I only know that the slope k of the point slope is the derivative of Y over X, The tangent vector of a curve, the normal vector of a surface. Why is one tangent vector and the other normal vector?

Total differential, f (x, y, z) = 0; DF (x, y (x), Z (x)) / DX = 0; fxdx + fydy (x) + fzdz (x) = 0; D is the reciprocal, f is the partial derivative. The reciprocal can determine the tangent vector. According to the nature of the vector, the product of the vertical vector is zero, so the partial derivative can determine the normal vector

What's the difference between normal vector and direction vector? What are they all for

Normal vector refers to the normal vector of a plane, which determines a plane and is perpendicular to the plane. Direction vector is the vector that determines a straight line and its direction

How is the normal vector of the tangent plane of this surface solved,