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<h2 class="title">Properties of Vectors</h2>
<p>Vectors are mathematical objects and we will now study some of their mathematical properties.</p>
<p>If two vectors have the same magnitude (size) <em>and</em> the same direction, then we call them equal to each other. For example, if we have two forces, \(\vec{F_{1}} = \text{20}\text{ N}\) <em>in the upward direction</em> and \(\vec{F_{2}} = \text{20}\text{ N}\) <em>in the upward direction</em>, then we can say that \(\vec{F_{1}} = \vec{F_{2}}\).</p>
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<h3>Definition: Equality of Vectors</h3>
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<p>Two vectors are equal if they have the <strong>same</strong> magnitude and the <strong>same</strong> direction.</p>
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<p>Just like scalars which can have positive or negative values, vectors can also be positive or negative. A negative vector is a vector which points in the direction <em>opposite</em> to the <strong>reference positive direction</strong>. For example, if in a particular situation, we define the upward direction as the reference positive direction, then a force \(\vec{F_{1}} = \text{30}\text{ N}\) <em>downwards</em> would be a <em>negative vector</em> and could also be written as \(\vec{F_{1}} = -\text{30}\text{ N}\). In this case, the negative sign (\(-\)) indicates that the direction of \(\vec{F_{1}}\) is opposite to that of the reference positive direction.</p>
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<h3>Definition: Negative Vector</h3>
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<p>A negative vector is a vector that has the <em>opposite</em> direction to the reference positive direction.</p>
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<p>Like scalars, vectors can also be added and subtracted. We will investigate how to do this next.</p>
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Properties of 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.


Properties of Vectors

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