<h2>Summary of the Graphical Method of Adding and Subtracting Vectors</h2>
<ul>
<li>The <strong>graphical method of adding vectors </strong>\(\mathbf{A}\) and \(\mathbf{B}\) involves drawing vectors on a graph and adding them using the head-to-tail method. The resultant vector \(\mathbf{R}\) is defined such that \(\mathbf{\text{A}}+\mathbf{\text{B}}=\mathbf{\text{R}}\). The magnitude and direction of \(\mathbf{R}\) are then determined with a ruler and protractor, respectively.</li>
<li>The <strong>graphical method of subtracting vectors </strong>\(\mathbf{B}\) from \(\mathbf{A}\) involves adding the opposite of vector \(\mathbf{B}\), which is defined as \(-\mathbf{B}\). In this case, \(\mathbf{A}–\mathbf{\text{B}}=\mathbf{\text{A}}+\left(\mathbf{–B}\right)=\mathbf{R}\). Then, the head-to-tail method of addition is followed in the usual way to obtain the resultant vector \(\mathbf{R}\).</li>
<li>Addition of vectors is <strong>commutative</strong> such that \(\mathbf{\text{A}}+\mathbf{\text{B}}=\mathbf{\text{B}}+\mathbf{\text{A}}\) .</li>
<li>The <strong>head-to-tail method</strong> of adding vectors involves drawing the first vector on a graph and then placing the tail of each subsequent vector at the head of the previous vector. The resultant vector is then drawn from the tail of the first vector to the head of the final vector.</li>
<li>If a vector \(\mathbf{A}\) is multiplied by a scalar quantity \(c\), the magnitude of the product is given by \(\text{cA}\). If \(c\) is positive, the direction of the product points in the same direction as \(\mathbf{A}\); if \(c\) is negative, the direction of the product points in the opposite direction as \(\mathbf{A}\).</li>
</ul>
<h2>Glossary</h2>
<h3>component (of a 2-d vector)</h3>
<p>a piece of a vector that points in either the vertical or the horizontal direction; every 2-d vector can be expressed as a sum of two vertical and horizontal vector components</p>
<h3>commutative</h3>
<p>refers to the interchangeability of order in a function; vector addition is commutative because the order in which vectors are added together does not affect the final sum</p>
<h3>direction (of a vector)</h3>
<p>the orientation of a vector in space</p>
<h3>head (of a vector)</h3>
<p>the end point of a vector; the location of the tip of the vector’s arrowhead; also referred to as the “tip”</p>
<h3>head-to-tail method</h3>
<p>a method of adding vectors in which the tail of each vector is placed at the head of the previous vector</p>
<h3>magnitude (of a vector)</h3>
<p>the length or size of a vector; magnitude is a scalar quantity</p>
<h3>resultant</h3>
<p>the sum of two or more vectors</p>
<h3>resultant vector</h3>
<p>the vector sum of two or more vectors</p>
<h3>scalar</h3>
<p>a quantity with magnitude but no direction</p>
<h3>tail</h3>
<p>the start point of a vector; opposite to the head or tip of the arrow</p>
<section data-element-type="conceptual-questions"></section>

1c4ddb66-ad36-4f81-90e7-4629f497d0b4

Summarizing the Graphical Method of Vector Addition and Subtraction

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.

Physics

Explore the principles of two-dimensional kinematics, including mastering vector addition and subtraction, resolving a vector into components, and analyzing projectile motion and relative velocities.


Summarizing the Graphical Method of Vector Addition and Subtraction

Track Your Learning Progress