Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 years ago

Determine the angle measure between vectors u and v?

U=4i-2j and v=i+3j

3 Answers

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  • 6 years ago
    Favorite Answer

    u = 4i - 2j

    tan(u) = - 2/4 = - 1/2 → angle_u = - 26.565°

    v = i + 3j

    tan(v) = 3/1 = 3 → angle_v = 71.565°

    angle between u and v:

    = 71.565 - (- 26.565)

    = 71.565 + 26.565

    = 98.130°

  • 6 years ago

    u.v = |u||v|cosθ

    Now, u.v => (4)(1) + (-2)(3) = -2

    |u| = √(4² + 2²) => √20

    |v| = √(1² + 3²) => √10

    so, -2 = √20√10 x cosθ

    => cosθ = -2/√200

    so, θ = cos⁻¹(-2/√200) => 98.1°

    :)>

  • lia l
    Lv 5
    6 years ago

    u=4i-2j and v=i+3j

    cos (angle between u and v)=

    (4i-2j )(i+3j )/length(u)*length(v)

    length(u)=sqrt(4^2+2^2)=sqrt20=2sqrt5

    length(v)=sqrt(1+3^2)=sqrt10=sqrt2*sqrt5

    cos (angle between u and v)

    =(4-6)/10sqrt2=-1/5sqrt2

    angle between u and v )=

    acos(-1/5sqrt2)=1.7

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