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27 June, 11:53

Given Bold u equals negative Bold i plus Bold j , Bold v equals 10 Bold i minus 2 Bold j , and Bold w equals negative 8 Bold j , find proj Bold Subscript u left parenthesis Bold v plus Bold w right parenthesis.

Given u=-i+j, v=10i-2j, and w = -8j

find proj Subscript u (v+w)

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Answers (2)
  1. 27 June, 12:14
    0
    Answer: u. (v+w) = - 20

    Step-by-step explanation:

    Given;

    u = - i+j

    v = 10i-2j

    w = - 8j

    v+w = 10i-2j + (-8j)

    v+w = 10i-10j

    u. (v+w) = (-i+j). (10i-10j)

    = - 1*10 + 1 * -10

    = - 10-10

    u. (v+w) = - 20
  2. 27 June, 14:06
    0
    Answer: u (v+w) = - 20

    Step-by-step explanation: u, v and w are vectors in the x-y plane, where i is related to the x-axis and j is related to the y-axis. Vectors can be added, subtracted or "perform" an operation called dot product.

    In this question, we have: u. (v + w)

    To resolve it, first add the vectors:

    (v + w) = (10i - 2j) + (-8j)

    (v + w) = (10i - 10j)

    Now, the dot product:

    u. (v + w) = (-i + j). (10i - 10j)

    u. (v + w) = (-1) (10) + (1). (-10)

    u. (v + w) = - 10 - 10

    u. (v + w) = - 20

    Note that the sum of vector gave another vector. However, the dot product of vectors produce a scalar because it's the sum of the product of the horizontal elements with the sum of the product of the vertical elements.
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