The grammar book says it is incorrect sentence, but doesn't mention the reason.
NOT A TEACHER
I thought that this information might interest some of my fellow learners.
""You look like your mother" = You and your mother have a
similar appearance (hair, eyes, nose, etc.).
According to my books, the sentence should be parsed like this:
You = subject.
look =
linking verb. (It is NOT an action verb, such as "He looks at a painting in the museum.")
like = this word in this sentence is
technically an adjective.
unto = this is the missing preposition that people NO longer use.
your mother = this noun phrase is the object of the "understood" preposition "unto."
Thus: You look like
unto your mother.
Compare: He looks like (unto) a nice person. I think that I can trust him. / She looks like (unto) a well-educated person. I think that she will have the correct answer to my question.