WEBVTT
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What is the magnitude of the vector ππ where π΄ equals 11, three and π΅ equals seven, three?
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The magnitude of a vector is its size or length.
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So in this case, we need to find the distance or length between point π΄ and point π΅.
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There are several ways of approaching this problem, we will look at two of them.
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Our first method will be graphically, and we will begin by plotting the two coordinates.
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Point π΄ has coordinates 11, three.
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Point π΅ has coordinates seven, three.
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As both points have the same π¦-coordinate, the distance from π΄ to π΅ will be a horizontal distance.
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To get from 11 to seven, we need to subtract four.
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As the magnitude of any vector must be positive, then the magnitude of ππ is equal to four.
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We could also have calculated the distance between point π΄ and point π΅ using one of our coordinate geometry formulas.
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The distance between any two points is equal to the square root of π₯ one minus π₯ two squared plus π¦ one minus π¦ two squared, where our two points have coordinates π₯ one, π¦ one and π₯ two, π¦ two.
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Substituting in our values gives us π is equal to the square root of 11 minus seven squared plus three minus three squared.
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It doesnβt matter which coordinate is π₯ one, π¦ one and which one is π₯ two, π¦ two.
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11 minus seven is equal to four, and three minus three is zero.
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As zero squared is equal to zero, π is equal to the square root of four squared.
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As our distance must be positive, this is equal to four.
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Once again, we have calculated that the magnitude of the vector ππ is four.
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Our final question will involve finding the magnitude of two separate vectors and their sum.