I am not sure how to proceed.
This is what I think: I know that the gradient is perpendicular to the level curve of a function. does that mean that the gradient at a point will be parallel to the tangent plane at that exact point? If so, that would mean that the normal of the plane $x+2y+3z = 1$ is perpendicular to the gradient. and then from that, I just set the dot product of the gradient and the normal vector to 0 to find where it happens.
However, I highly doubt my approach and it made me realize that I don't really understand the geometric meaning of the gradient. Thus, can someone please how should i approach this problem intuitively.
