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Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Consider the vectors: u = ⟨−2,a,1⟩ and v = ⟨4,0,b⟩ where a and b are positive numbers. Find a and b if ||u-v||=sqrt(61), and ||v||=5?

2 Answers

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  • ?
    Lv 7
    1 month ago

    Hint: First, evaluate ||b||.  This is something you should be able to do since it's basically something we learned in early high school. It's nothing new.

    Once you've answered, then we will take it from there if need be.

    Hopefully no one will spoil you the answers. That would be very irresponsible of them. And don't forget to vote me best answer for being the first to correctly walk you through without spoiling the answers. That way it gives you a chance to work at it and to get good at it.

    By the way, it's very impolite to be anonymous here, And there is no reason to be anonymous here. Besides, if you are not Anonymous, you would get more answers.

  • 1 month ago

    1st v

    sqrt(4^2 + 0^2 + b^2) = 5

    4^2 + b^2 = 25

    b = 3

    u = <-2, a, 1>

    v = <4, 0, 5>

    u-v = <-6, a, 4>

    sqrt((-6)^2 + a^2 + 4^2) = sqrt(61)

    (-6)^2 + a^2 + 4^2 = 61

    36 + a^2 + 16 = 61

    a^2 = 9

    a = +/- 3

    u = ⟨−2, +/- 3, 1⟩ and v = ⟨4, 0, 5⟩

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