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22 September, 13:16

Given that P (5,4), Q=7,3), R = (8,6) and S = (4,1) find the component from of the vector PQ+5RS

Use the information from above to find the magnitude of the vector PQ+5RS

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Answers (1)
  1. 22 September, 16:17
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    For this case we have the following ordered pairs:

    P (5.4)

    Q = 7.3)

    R = (8.6)

    S = (4.1)

    For the PQ vector we have:

    PQ = Q-P = (7, 3) - (5, 4)

    PQ = (2, - 1)

    For the RS vector we have:

    RS = S-R = (4, 1) - (8, 6)

    RS = (-4, - 5)

    Then the vector PQ + 5RS is given by:

    PQ + 5RS = (2, - 1) + 5 (-4, - 5)

    PQ + 5RS = (2, - 1) + (-20, - 25)

    PQ + 5RS = (-18, - 26)

    Finally, the magnitude of the vector is:

    lPQ + 5RSl = root (( - 18) ^ 2 + (-26) ^ 2)

    lPQ + 5RSl = 31.6

    Answer:

    Vector:

    PQ + 5RS = (-18, - 26)

    Magnitude:

    lPQ + 5RSl = 31.6
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