Find the angle between u and v.?

Find the angle between u and v. Let u = (3,-2,1) and v = (2,-3,1)

3 Answers

Relevance
  • 9 years ago
    Best Answer

    u = <3, -2, 1 > and v = <2, -3, 1

    II u II = √(9+4+1) = √14

    II v II = √(4+9+1) = √14

    θ = cos^-1 [ u.v / II u II II v II ]

    = cos^-1 [(3*2 + (-2*-3) + (1*1)) /14 ]

    = cos^-1(13/14)

    = 21.79°

  • a * b = |a| |b| cosθ

    <3, -2, 1> * <2, -3, 1> = sqrt(1^2 + 2^2 + 3^2) * sqrt(1^2 + 2^2 + 3^2) * cosθ

    6 + 6 + 1 = 14 * cosθ

    13/14 = cosθ

    θ = arccos(13/14)

    θ = 0.380 rad

    θ = 21.79 deg

  • Kevin
    Lv 6
    9 years ago

    21.79°

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