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Math Help - Vector in Component

  1. #1
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    Vector in Component

    For this question, p=0.6i-aj, q=bi+cj, r=di+ej and s=fi+gj
    find the possible values of a b c d e f and g given that

    • p is a unit vector and a is a positive constant
    • q is in the same direction as p and 5 times the magnitude
    • r+2q=11i-20j
    • s is in the same direction as r but equal in magnitude to q
    thnx
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  2. #2
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    Hi, Fibonacci. What have you tried so far? Do you know how to find the magnitude (norm) of a vector? If so, you can use the conditions given to form a set of equations.

    Let me get you started:
    We are told that p=0.6\textbf{i}-a\textbf{j}, where p is a unit vector, which means its magnitude is 1, and a is positive.

    Since \lVert p\rVert = 1, we have

    \lVert p\rVert = \sqrt{0.6^2+a^2} = 1

    \implies \sqrt{0.36+a^2} = 1

    Square both sides:

    0.36+a^2 = 1\implies a^2 = 0.64

    \implies a=\pm\sqrt{\frac{64}{100}}=\pm\frac{4}{5}

    And since a>0, you can discard the negative solution. Does that help?
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  3. #3
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    yes, i'll try and see if i can work out the other part of the question now

    thank u
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