What about adding vectors that move in different directions? The example above only shows the addition of vectors moving in the same direction.

<h2>Adding Vectors</h2>
<section>
<p>When vectors are added, we need to take into account <em>both</em> their magnitudes <em>and</em> directions.</p>
<p>For example, imagine the following. You and a friend are trying to move a heavy box. You stand behind it and push forwards with a force \(\vec{{F}_{1}}\) and your friend stands in front and pulls it towards them with a force \(\vec{{F}_{2}}\). The two forces are in the <em>same</em> direction (i.e. forwards) and so the total force acting on the box is:</p>
<img alt="865324f93757a5017f2a7dcf8f906d82.png" src="https://data.ulearngo.com/assets/0e19fffa-b2fe-466b-8f4e-8c8e06585a18"/>
<p>It is very easy to understand the concept of vector addition through an activity using the <strong>displacement</strong> vector.</p>
<p>Displacement is the vector which describes the change in an object's position. It is a vector that points from the initial position to the final position.</p>
<div class="ns-school-emp">
<h2>Optional Activity: Adding Vectors</h2>
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<h3 class="title">Materials</h3>
<section class="activity">
<p>masking tape</p>
</section>
<section class="activity">
<h3>Method</h3>
<p>Tape a line of masking tape horizontally across the floor. This will be your starting point.</p>
<p><em>Task 1</em>:</p>
<p>Take \(\text{2}\) steps in the forward direction. Use a piece of masking tape to mark your end point and label it <strong>A</strong>. Then take another \(\text{3}\) steps in the forward direction. Use masking tape to mark your final position as <strong>B</strong>. Make sure you try to keep your steps all the same length!</p>
<p><em>Task 2</em>:</p>
<p>Go back to your starting line. Now take \(\text{3}\) steps forward. Use a piece of masking tape to mark your end point and label it <strong>B</strong>. Then take another \(\text{2}\) steps forward and use a new piece of masking tape to mark your final position as <strong>A</strong>.</p>
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<section class="activity">
<h3>Discussion</h3>
<p>What do you notice?</p>
<ol>
<li>
<p>In <em>Task 1</em>, the first \(\text{2}\) steps forward represent a displacement vector and the second \(\text{3}\) steps forward also form a displacement vector. If we did not stop after the first \(\text{2}\) steps, we would have taken \(\text{5}\) steps in the forward direction in total. Therefore, if we add the displacement vectors for \(\text{2}\) steps and \(\text{3}\) steps, we should get a total of \(\text{5}\) steps in the forward direction.</p>
</li>
<li>
<p>It does not matter whether you take \(\text{3}\) steps forward and then \(\text{2}\) steps forward, or two steps followed by another \(\text{3}\) steps forward. Your final position is the same! The order of the addition does not matter!</p>
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</ol>
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</section>
<section class="activity"></section>
<section class="activity"></section>
<p>We can represent vector addition graphically, based on the activity above. Draw the vector for the first two steps forward, followed by the vector with the next three steps forward.</p>
<p><img alt="3e0425450e0f70a29c195a2cb52722a8.png" src="https://data.ulearngo.com/assets/4dfe4ad0-17b0-4a25-af0e-d09dc358e08a"/></p>
<p>We add the second vector at the end of the first vector, since this is where we now are after the first vector has acted. The vector from the tail of the first vector (the starting point) to the head of the second vector (the end point) is then the sum of the vectors.</p>
<p>As you can convince yourself, the order in which you add vectors does not matter. In the example above, if you decided to first go \(\text{3}\) steps forward and then another \(\text{2}\) steps forward, the end result would still be \(\text{5}\) steps forward.</p>
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Adding Vectors

Physics is a science discipline concerned with the nature and properties of matter and energy. Physics topics include mechanics, heat, light and radiation, sound, electricity, magnetism, the structure of atoms, and so on.

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Discover the principles and operations of scalars and vectors such as graphical and algebraic techniques of vector addition, finding magnitude with Pythagoras theorem, and resultant force on a submarine.


Adding Vectors

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