WEBVTT
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Consider two vectors: π and π.
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π equals negative seven π’ hat minus seven π£ hat and π equals negative six π’ hat minus two π£ hat.
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Calculate π plus π.
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This question gives us two vectors in component form, and it asks us to calculate their sum.
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Our first vector is π, which equals negative seven π’ hat minus seven π£ hat.
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Since π’ hat is the unit vector in the π₯-direction and π£ hat is the unit vector in the π¦-direction, this means that π extends negative seven units in the π₯-direction and negative seven units in the π¦-direction.
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So, vector π looks like this.
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Our second vector is π, which equals negative six π’ hat minus two π£ hat.
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This means that vector π extends negative six units in the π₯-direction and negative two units in the π¦-direction.
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So it looks like this.
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Now we need to add these two vectors together.
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The question gives us these vectors in component form.
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And in this case, the simplest way to add these two vectors is to do it algebraically.
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To do this, we add together the π₯-components and the π¦-components of the two vectors separately.
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The result of this, the sum of these two vectors, is known as their resultant.
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So letβs take our two vectors π and π and add together their π₯- and π¦-components.
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If we add together the π₯-components to get the π₯-component of our resultant vector, we have negative seven plus negative six.
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Since this is the π₯-component, we multiply this by π’ hat.
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Then if we add the π¦-components, we have negative seven plus negative two.
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And this gets multiplied by π£ hat.
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The final step is to evaluate these sums for the π₯-component and the π¦-component.
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For the π₯-component, adding together negative seven and negative six gives us a result of negative 13.
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And for the π¦-component, adding negative seven and negative two gives us negative nine.
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And so we find that the sum or the resultant of the vectors π and π is equal to negative 13π’ hat minus nine π£ hat.