Given vectors u = ⟨2, –3⟩ and v = ⟨1, –1⟩, what is the measure of the angle between the vectors?

Question

Given vectors u = ⟨2, –3⟩ and v = ⟨1, –1⟩, what is the measure of the angle between the vectors?

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Thành Đạt 3 years 2021-08-27T08:21:45+00:00 2 Answers 0 views 0

Answers ( )

  1. thongdat2
    0
    2021-08-27T08:23:00+00:00
    Reply

    Answer:

    The Answer is A. 11.3

    Step-by-step explanation:

    got it right. Also thats just the letter answer  🙂

  2. Maris
    0
    2021-08-27T08:23:06+00:00
    Reply

    Answer:

    The measure of the angle between the vectors = Ф = 11.30°

    Step-by-step explanation:

    Given

    • u = ⟨2, –3⟩
    • v = ⟨1, –1⟩

    \mathrm{Computing\:the\:angle\:between\:the\:vectors}:\quad \cos \left(\theta \right)\:=\frac{\vec{a\:}\cdot \vec{b\:}}{\left|\vec{a\:}\right|\cdot \left|\vec{b\:}\right|}

    Next, find the lengths of the vectors:

    \mathrm{Computing\:the\:Euclidean\:Length\:of\:a\:vector}:\quad \left|\left(x_1\:,\:\:\ldots \:,\:\:x_n\right)\right|=\sqrt{\sum _{i=1}^n\left|x_i\right|^2}

    u = ⟨2, –3⟩

    \:\:\left|u\right|\:=\sqrt{2^2+\left(-3\right)^2}

         =\sqrt{13}

    u = ⟨2, –3⟩

    |v|=\sqrt{1^2+\left(-1\right)^2}

        =\sqrt{2}

    Finally, the angle is given by:

    \mathrm{Computing\:the\:angle\:between\:the\:vectors}:\quad \cos \left(\theta \right)\:=\frac{\vec{a\:}\cdot \vec{b\:}}{\left|\vec{a\:}\right|\cdot \left|\vec{b\:}\right|}

    cos (Ф) = 5/√26

    Ф = arc cos (cos (Ф)) = arc cos (5 √26) / (26)

    Ф = 11.30°

    Thus, the measure of the angle between the vectors = Ф = 11.30°

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