Head-to-Tail Vector Addition - Questions 1 Help

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Vectors can be added together in step-wise fashion using a head-to-tail diagram. The first vector is drawn with its indicated direction and magnitude. The second vector is then added such that its tail (beginning) is placed at the head (arrowhead) of the first vector. This process is repeated for the third vector, with its tail being positioned at the head of the second vector. Once all three vectors have been added in this head-to-tail method, the resultant is drawn from the tail of the first vector to the head of the third vector.

There are 18 questions in this Concept Builder. They are all pretty much the same. You have to determine which diagram is the proper head-to-tail addition diagram for the addition of three vectors. Each vector is displayed; the magnitude and direction is shown. Here is one of the 18 questions:

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

The Basic Idea section above describes the general principle for adding vectors using the head-to-tail method. Your task in this question involves identifying the correct diagram that illustrates the addition of the three vectors in the equation. Here are some details that you will need to pay attention to in order to discriminate between the correct diagram and five incorrect ones.

Head ... to ... Tail
The first detail is to pay attention is the adherence to the head-to-tail approach. This approach is described in The Basic Ideas section above. In general, if you see two of the three vectors in the equation with their tails touching or their arrowheads touching, then it is not a correct digram.

Pay Attention to Order
Give attention to the order in which the vectors have been added. If the equation is A + B + C = ??? then one would expect to see Vector B being added onto the end of vector A and vector C being added onto the end of Vector B. If not, then the diagram is wrong. (Even though A + B + C gives the same resultant as A + C + B, if the question is asking you to find the A + B + C diagram, then don't pick the A + C + B diagram.)

Vectors Keep Their Direction
The vector addition equation shows the picture for the three vectors that must be added. These vectors keep their direction when added together. That is, if Vector B is in the equation and if it has a northwest direction, then it should keep its northwest direction when added to another vector. Adding a vector doesn't change that vector's direction.

Know the Result
The resultant's direction matters! It should be drawn from the tail of the first vector to the head of the third vector. If it isn't, then don't pick that diagram.

Getting Started
Sometimes it is difficult getting started with these types of questions. The following might help. Look at the first vector in the equation; then look for it in the diagram (the answer option). Focus on that vector. Then make sure the second vector in the equation is added to this vector. And so on.

Try these links to The Physics Classroom Tutorial for more help with the process of adding vectors:

Vector Addition

Resultants