How to using jQuery function

How to using jQuery function

I'm using this jQuery function but when user press login and the username or password is incorrec, how am I show the error message? Becuase when user click submit button it will redirect to login_validation.php to do the verification checking. And in the login_verification.php I'm using if..else statement to do. How am I going to show error if the username or password is wrong and I want it pop out in the login page not the other page.
  1.   <script>
            jQuery(document).ready(function(){
                // binds form submission and fields to the validation engine
                jQuery("#formID").validationEngine();
               
                $("#formID").bind("jqv.form.validating", function(event){
                    $("#hookError").html("")
                })

                $("#formID").bind("jqv.form.result", function(event , errorFound){
                    if(errorFound) $("#hookError").append("Invalid username or password.");
                })
            });

            /**
            *
            * @param {jqObject} the field where the validation applies
            * @param {Array[String]} validation rules for this field
            * @param {int} rule index
            * @param {Map} form options
            * @return an error string if validation failed
            */
            function checkHELLO(field, rules, i, options){
                if (field.val() != "HELLO") {
                    // this allows to use i18 for the error msgs
                    return options.allrules.validate2fields.alertText;
                }
            }
        </script>