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Consider two vectors π and π, where π equals eight π’ hat minus four π£ hat and π equals negative two π’ hat plus five π£ hat.
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Calculate π minus π.
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So in this question, weβre given two vectors π and π in component form and weβre asked to calculate π minus π.
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So thatβs the result when we subtract the vector π from the vector π.
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Looking at our two vectors π and π, then if we recall that π’ hat is the unit vector in the π₯-direction and π£ hat is the unit vector in the π¦-direction, then we can see that each of our vectors has an π₯-component and a π¦-component.
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We should recall that if we want to subtract one vector from another, then we can do this by subtracting the π₯- and the π¦-components of those vectors separately.
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With this in mind, we can calculate π minus π.
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If we first subtract the π₯-components, then we see that we have the π₯-component of π, which is eight, minus the π₯-component of π, which is negative two.
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So our π₯-component of π minus π is equal to eight minus negative two.
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And since itβs an π₯-component, we multiply this by the unit vector π’ hat.
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Then, if we subtract the π¦-components, we have the π¦-component of π, which is negative four, minus the π¦-component of π, which is five.
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So our π¦-component of π minus π is equal to negative four minus five.
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And this π¦-component gets multiplied by the unit vector π£ hat.
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Then, evaluating our π₯- and π¦-components, we find that the π₯-component eight minus negative two gives us 10 and the π¦-component negative four minus five gives us negative nine.
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And so we found our answer to the question that when we calculate π minus π, our result is 10π’ hat minus nine π£ hat.