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let p=(1,1,1), Q=(2,3 5), and R=(-1,3,1). find the area A of thr triangle with vertices P,Q, and R

  • calculas -

    get the sides of the triangle, then use Heron's formula:

    PQ = √(1^2+2^2+4^2) = √21
    QR = √(3^2+0^2+4^2) = 5
    RP = √(2^2+2^2+0^2) = √8

    I'll let you use Heron's formula. Probably better to convert to decimals rather than having all those nested roots.

  • OR - calculus -

    area of triange = (1/2)|vector PQ x vector PR|

    vector PQ = [1,2,4] and vector PR = [-2, 2,0}
    PQ X PR = [-8,-8,6]
    area = (1/2)√(64+64+36) = 1/2 √164
    = 1/2 (2√41) = √41

  • calculus - duh -

    good job, Reiny. Forgot about vectors!

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