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If vector π΄ is equal to four π plus four π minus five π and vector π΅ is equal to three π minus π, determine the magnitude or modulus of vector π΄ minus vector π΅.
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Well in this problem, the first thing we want to do is vector π΄ minus vector π΅.
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And when we do this, so when we subtract vector π΅ from vector π΄, what we do is we deal with each individual components separately.
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So first of all, we have four minus three π.
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And then we add on four minus zero π.
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And thatβs because you get four from four π in vector π΄ and then zero because there is no π component to vector B.
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And then finally, we add on negative five minus negative one π.
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And thatβs because you get negative five in vector π΄ and then negative π, so negative one, from vector π΅.
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So we can say that vector π΄ minus vector π΅ is gonna be equal to π as our first term.
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And thatβs because we had four minus three which is just one.
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So itβs just π plus four π and then minus four π.
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And thatβs because we had negative five minus negative one.
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Well, minus a negative is an add.
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So you get negative five add one which is negative four.
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So now what we need to do is we need to find the magnitude or the modulus of vector π΄ minus vector π΅.
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Well, what is the magnitude?
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Well, if you want to find the magnitude of a vector, then itβs equal to the square root of π₯ squared plus π¦ squared plus z squared where these are the coefficients of π, π, and π.
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So, therefore, the magnitude of vector π΄ minus vector π΅ is gonna be equal to one squared plus four squared plus negative four squared.
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And thatβs because these were the coefficients of π, π, and π, respectively.
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So, therefore, this is gonna be equal to the square root of one plus 16 plus 16 which is gonna be equal to root 33.
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So, therefore, we can say that if vector π΄ is equal to four π plus four π minus five π and vector π΅ is equal to three π minus π, then the magnitude of vector π΄ minus vector π΅ is going to equal to root 33.