Vector A= 3.7 i + 1.0 j and vector B = 3.0 i + 6.5 j. What is vector (A-B).A?

Question

Vector A= 3.7 i + 1.0 j and vector B = 3.0 i + 6.5 j. What is vector
(A-B).A?

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Kiệt Gia 4 years 2021-07-26T08:39:00+00:00 1 Answers 10 views 0

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  1. Sapo1
    0
    2021-07-26T08:40:28+00:00
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    Answer:

    (A – B).A = -2.91

    Explanation:

    First, let’s define the sum and dot product of vectors.

    For two vectors V = (x₁, y₁) and W = (x₂, y₂) we have:

    sum (or subtraction):

    V + W = (x₁, y₁) +  (x₂, y₂)  = (x₁ + x₂, y₁ + y₂)

    dot product:

    V.W =  (x₁, y₁).(x₂, y₂) = x₁*x₂ + y₁*y₂

    Here remember the notation:

    V = x₁*i + y₁*j =  (x₁, y₁)

    Now let’s solve our problem, we have:

    A = (3.7, 1.0)

    B = (3.0, 6.5)

    Then:

    (A – B).A = (  (3.7, 1.0) –  (3.0, 6.5) ).(3.7, 1.0)

                  = (3.7 – 3.0, 1.0 – 6.5).(3.7, 1.0)

                  = (0.7, -5.5).(3.7, 1.0) = (0.7*3.7) + (-5.5)*(1.0) = -2.91

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