WEBVTT
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Some vectors are drawn to scale on a square grid.
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Which of the vectors 1, 2, 3, or 4 is the resultant of the vectors π and π?
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So here we have the square grid with a number of vectors drawn in.
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Hereβs vector 1, hereβs vector 2, hereβs number 3, and hereβs number 4.
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These are all candidates for the vector that results from adding vector π, shown here, with vector π, shown here.
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So the question is, if we add together π and π, then which of these four vectors do we get?
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Now looking at this grid, we can see that vector π is a completely vertical vector.
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That is, it has no horizontal component.
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And likewise, vector π is a purely horizontal vector with no vertical component.
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If we add these two vectors together, we can see that the resultant will have both a vertical and a horizontal component to it.
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It must because when we combine π and π, we have both of those components.
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This eliminates a few of our answer options.
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We can see, for example, that vector 1 only has a vertical and no horizontal component.
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Therefore, it wonβt be our answer.
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And then down at the bottom of our grid, we have vector 4, which has only a horizontal and no vertical component.
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Therefore, we know this wonβt be our choice either.
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Now we want to figure out whether to identify vector 3 or vector 2 as the resultant of vectors π and π.
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To do that, weβll use the grid spacings marked out on the square grid.
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Starting at the origin, where the tails of vector π and vector π meet.
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What weβll do is weβll count grid spaces from this point until we get to the head of vector π and vector π, respectively.
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Letβs start by moving horizontally out to the tip of vector π.
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Beginning at the origin, we count one grid space, two grid spaces, three, four, and then five.
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This means that our resultant vector, the vector that comes from adding vector π and vector π, will also have five horizontal spaces to it.
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And then doing the same thing on the vertical axis towards the tip of vector π, we once again start at the origin and then count up grid spaces.
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One, two, three, four, and again five.
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So the resultant of vectors π and π will have five grid spaces in the horizontal direction and five in the vertical direction.
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And of our two remaining candidates, vectors 3 and 2, we can see that itβs vector 3 that meets this test.
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Starting at the origin, if we move out one, two, three, four, five spaces in the horizontal direction.
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And then one, two, three, four, five spaces in the vertical direction.
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We reach this point here, which is at the tip of vector 3.
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And we see that the tail of vector 3 is at the origin.
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So vector 3 is the one which is the resultant of the vectors π and π.
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Vector 3 then is the answer we choose.