<section>
<h2 class="title">Sketching Tail-to-Tail Method</h2>
<p>In this method we draw the two vectors with their tails on the origin. Then we draw a line parallel to the first vector from the head of the second vector and vice versa. Where the parallel lines intersect is the head of the resultant vector that will also start at the origin. We will only deal with perpendicular vectors but this procedure works for any vectors.</p>
<div class="ns-school-defn2">
<h3>Fact:</h3>
<p>When dealing with more than two vectors the procedure is repetitive. First find the resultant of any two of the vectors to be added. Then use the same method to add the resultant from the first two vectors with a third vector. This new resultant is then added to the fourth vector and so on, until there are no more vectors to be added.</p>
</div>
<p>Let us apply this procedure to the same two vectors we used to illustrate the head-to-tail method:</p>
<ul>
<li>\(\vec{F}_{1} = \text{2}\text{ N}\) in the positive \(y\)-direction</li>
<li>\(\vec{F}_{2} = \text{1.5}\text{ N}\) in the positive \(x\)-direction</li>
</ul>
<p>We first draw a Cartesian plane with the first vector originating at the origin:</p>
<img alt="6d845a34bc851dd4f5f1e63519573df1.png" src="https://data.ulearngo.com/assets/ecb75c6e-369f-438e-9319-d751f6610ca3"/>
<p>Then we add the second vector but also originating from the origin so that the vectors are drawn tail-to-tail:</p>
<img alt="35f11a7900287a822125ce1b15955235.png" src="https://data.ulearngo.com/assets/6da57761-512c-4c6d-bd34-963f6343b9fc"/>
<p>Now we draw a line parallel to \(\vec{F}_{1}\) from the head of \(\vec{F}_{2}\):</p>
<img alt="fd90f5d7a2243a0f35c7f1db70cf5dc1.png" src="https://data.ulearngo.com/assets/13342ea1-0184-4169-b097-820bc3bb2f43"/>
<p>Next we draw a line parallel to \(\vec{F}_{2}\) from the head of \(\vec{F}_{1}\):</p>
<img alt="2bbd636b22187839d32e84c2329ca2ae.png" src="https://data.ulearngo.com/assets/4a7f1346-c63c-49ab-831d-e15e9f9b9c7b"/>
<p>Where the two lines intersect is the head of the resultant vector which will originate at the origin so:</p>
<img alt="1f489c4637b429a90dacd22a6a617790.png" src="https://data.ulearngo.com/assets/df14e886-bb16-4cd7-8b2f-2e53d1136ea5"/>
<p>You might be asking what you would do if you had more than 2 vectors to add together. In this case all you need to do is first determine \(\vec{R}_{x}\) by adding all the vectors that are parallel to the \(x\)-direction and \(\vec{R}_{y}\) by adding all the vectors that are parallel to the \(y\)-direction. Then you use the tail-to-tail method to find the resultant of \(\vec{R}_{x}\) and \(\vec{R}_{y}\).</p>
</section>
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Sketching Tail-to-Tail Method

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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.


Sketching Tail-to-Tail Method

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