<h2>Summary</h2>
<ul>
<li>The analytical method of vector addition and subtraction involves using the Pythagorean theorem and trigonometric identities to determine the magnitude and direction of a resultant vector.</li>
<li>The steps to add vectors \(\mathbf{A}\) and \(\mathbf{B}\) using the analytical method are as follows:

<p>Step 1: Determine the coordinate system for the vectors. Then, determine the horizontal and vertical components of each vector using the equations</p>
<div>\({A}_{x} = A\text{ cos }\theta\)<br/>
\({B}_{x} = B\text{ cos }\theta\)</div>
<p>and</p>
<div>\({A}_{y} = A\text{ sin }\theta\)<br/>
\({B}_{x} = B\text{ sin }\theta\)</div>
<p>Step 2: Add the horizontal and vertical components of each vector to determine the components \({R}_{x}\) and \({R}_{y}\) of the resultant vector, \(\mathbf{\text{R}}\):</p>
<div>\({R}_{x}={A}_{x}+{B}_{x}\)</div>
<p>and</p>
<div>\({R}_{y}={A}_{y}+{B}_{y.}\)</div>
<p>Step 3: Use the Pythagorean theorem to determine the magnitude, \(R\), of the resultant vector \(\mathbf{\text{R}}\):</p>
<div>\(R=\sqrt{{R}_{x}^{2}+{R}_{y}^{2}}.\)</div>
<p>Step 4: Use a trigonometric identity to determine the direction, \(\theta \), of \(\mathbf{\text{R}}\):</p>
<div>\(\theta ={\text{tan}}^{-1}\left({R}_{y}/{R}_{x}\right).\)</div>
</li>
</ul>
<h2>Glossary</h2>
<h3>analytical method</h3>
<p>the method of determining the magnitude and direction of a resultant vector using the Pythagorean theorem and trigonometric identities</p>
<section data-element-type="conceptual-questions"></section>

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Summarizing the Analytical 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.

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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 Analytical Method of Vector Addition and Subtraction

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