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The angle between vector π and vector π is equal to 22 degrees.
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If the magnitude of vector π equals three and the magnitude of vector π equals 25.2, find the dot product of vector π and π to the nearest hundredth.
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When dealing with the angle between two vectors, we recall that the cos of this angle π is equal to the dot product of the two vectors divided by the product of the magnitude of the two vectors.
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In this question, weβre told that the angle is 22 degrees.
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The magnitude of vector π is equal to three.
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The magnitude of vector π is equal to 25.2.
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We need to work out the value of the dot product of vector π and vector π.
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Substituting in our values gives us cos of 22 degrees is equal to the dot product of vectors π and π divided by three multiplied by 25.2.
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Three multiplied by 25.2 is equal to 75.6.
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We can then multiply both sides of the equation by 75.6.
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The dot product of vectors π and π is equal to 75.6 multiplied by the cos of 22 degrees.
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This is equal to 70.0950 and so on.
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We have been asked to round our answer to the nearest hundredth.
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This is the same as rounding to two decimal places.
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As our deciding number is a five, we round up.
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Therefore, the dot product of vectors π and π is 70.10.