Head-to-Tail Vector Addition

The Head-to-Tail Vector Addition Concept Builder is comprised of 18 questions that are organized into nine Question Groups and spread across three difficulty levels. Every question involves an identical task. The questions are different but the task is identical. Students are given a diagram of three vectors and a vector addition equation; they must identify the proper head-to-tail addition diagram for adding the three vectors in the order in which they are given. There are six answer options to select from. Students can tap on the diagram to toggle through the six options and then to cycle back through them again. 

There are two questions in every Question Groups.  If a student misses a question within a Question Group, then he/she will have to answer that question and the other question in the same Group in order to be "done" with that Group.The three difficulty levels are only distinguished in difficulty by the number of required questions that must be answered. The questions in the Wizard Difficulty Level are no more difficult than the questions in the Master or Apprentice Difficulty Levels. It's just that the Wizard Difficulty Level includes nine questions while the Master Level includes six questions and the Apprentice Level only includes three questions. In fact, the nine Question Groups of the Wizard Difficulty Level include the six Question Groups of the Master Difficulty Level plus three additional Question Groups. 

Teachers are encouraged to either do the activity or view the questions (below) to make a judgement about the suitability of the Difficulty Level for their classes. We have not provided the answer options below so we recommend that a teacher do the Concept Builder in order to get a feel for the difficulty of the task.

The Physics Classroom grants teachers and other users the right to print these questions for private use. Users are also granted the right to copy the text and modify it for their own use. However, this document should not be uploaded to other servers for distribution to and/or display by others. The Physics Classroom website should remain the only website or server from which the document is distributed or displayed. We also provide a PDF that teachers can use under the same conditions. We have included a link to the PDF near the bottom of this page.

 

 

Head to Tail Addition

 
Question Group 1
Question 1
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 
Question 2
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 
Question Group 2
Question 3
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 
Question 4
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 
Question Group 3
Question 5
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 
Question 6
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 

 
Question Group 4
Question 7
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 
Question 8
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 
Question Group 5
Question 9
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 

 
Question 10
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 
Question Group 6
Question 11
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
Question 12
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 

 
Question Group 7
Question 13
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 
Question 14
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 
Question Group 8
Question 15
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 

 
Question 16
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 
 
Question Group 9
Question 17
Identify the correct head-to-tail vector addition diagram for this vector addition equation:
 

 
 
Question 18
Identify the correct head-to-tail vector addition diagram for this vector addition equation: