Matematika

Pertanyaan

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1 Jawaban

  • 34. A=(1,0,2), B=(5,4,10), C=(4,6,4)
    P=(3B+A)/4
    =(3(5,4,10)+(1,0,2)/4
    =(16,12,32)/4
    P=(4,3,8)
    PC=C-P -->(4,6,4)-(4,3,8)=(0,3,-4)
    AB=B-A -->(5,4,10)-(1,0,2)=(4,4,8)
    |AB|=√(16+16+64)=√96=4√6
    maka:
    |ē|=(PC.AB)/|AB|
    =((0,3,-4).(4,4,8))/4√6
    =(12-32)/4√6
    = -20/4√6
    = -5/√6 = (-5√6)/6
    35. a=(2,-2,4), b=(4,2,p), |ē|=(8√5)/5
    |ē|= (a.b)/|b|
    (8√5)/5=((2,-2,4).(4,2,p))/√(4²+2²+p²)
    (8√5)(√20+p²)=5(4+4p)
    8√(100+5p²)=20+20p <---dikuadratkan
    64(100+5p²)=400p²+800p+400
    6400+320p²=400p²+800p+400
    400p²-320p²+800p+400-6400=0
    80p²+800p-6000=0<----dibagi 40
    2p²+20p-150=0
    (2p+30)(p-5)
    ->p= -15
    ->p=5
    yg memenuhi jika dimasukan dalam rumus adalah 5, maka {p=5}