Hi Guys,
Below is the code of my VF page and my controller and i am getting a null pointer exception.I am new to apex and VF development .
Please let me know where i am going wrong and help me in this regard.
Thanks in anticipation.

VF Page :


<apex:page controller="ShowHideController"> <!-- controller="AccountController" -->
<apex:form >
<apex:pageBlock title="Select the options"> Vehicle Names&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <apex:selectList value="{!selectedVehicleId}" size="1">
<apex:selectOptions value="{!VehicleType}"/>
<apex:actionSupport event="onchange" reRender="a"/>
</apex:selectList> Available parts &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<apex:pageBlockSection id="a">
<apex:selectList value="{!selectedBikePartId}" size="5">
<apex:selectOptions value="{!BikeParts}"/>
</apex:selectList>
</apex:pageBlockSection>
</apex:pageBlock>
</apex:form>
</apex:page>

Controller :
public class ShowHideController {
    public String selectedVehicleId{get;set;} 
    public String selectedBikePartId{get;set;}
     // this var is available only in the view and not seen in the
    //  controller methods below
    
    
    public ShowHideController(){
        
        
        
    }
    
    public List<SelectOption> getVehicleType() {
                List<SelectOption> vehicletypelist= new List<SelectOption>();
                  vehicletypelist.add( new SelectOption('','--Select--'));
                  for( Vehicle__c ve : [select Id,VehicleType__c from Vehicle__c ]) {
                          vehicletypelist.add( new SelectOption(ve.Id,ve.VehicleType__c));
                  }
                 return vehicletypelist;
           }
    public List<SelectOption> getBikeParts(){
        List<SelectOption> bikepartlist=new List<SelectOption>();
        List<SelectOption> options= new List<SelectOption>();
            if(selectedVehicleId!=null && selectedVehicleId=='Bike'){
                for(Vehicle__c ve2:[select Id,Bike_parts_available__c from Vehicle__c where VehicleType__c=:selectedVehicleId ]){
                    bikepartlist.add(new SelectOption(ve2.Id,ve2.Bike_parts_available__c));
                    
                }
                }
                 else
                    {
                        bikepartlist.add( new SelectOption('--None--','--None--'));
                    }
            
        
        return bikepartlist;
    }

//Below code is not implemented
    public List<SelectOption> getCarParts(){
        List<SelectOption> carpartlist=new List<SelectOption>();
        List<SelectOption> options= new List<SelectOption>();
            if(selectedVehicleId!=null && selectedVehicleId=='car'){
                for(Vehicle__c ve3:[select Id,Car_parts_available__c from Vehicle__c where VehicleType__c=:selectedVehicleId]){
                    carpartlist.add(new SelectOption(ve3.Id,ve3.Car_parts_available__c));
                    
                }     
            }
        
        return carpartlist;
    }
    
}