Находим векторы: <span>
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Вектор АВ={xB-xA, yB-yA, zB-zA} 1 -1 -5 </span></span>√<span><span>27 = 5,196152423
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Вектор
BC={xC-xB, yC-yB, zC-zB}
-3 -2 0 </span></span>√<span><span>13 = 3,605551275
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Вектор
АC={xC-xA, yC-yA, zC-zA} -2 -3
-5 </span></span>√<span><span>38 = 6,164414003
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Вектор
АD={xD-xA, yD-yA, zD-zA}
-5 3 -9 </span></span>√<span><span>115 = 10,72380529
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Вектор
BD={xD-xB, yD-yB, zD-zB}
-6 4 -4 </span></span>√<span><span>68 = 8,246211251
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Вектор
CD={xD-xC, yD-yC, zD-zC} -3 6 -4 </span></span>√<span>61 = 7,810249676. </span><span>
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Произведение векторов
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<span>a × b =
{aybz - azby; azbx - axbz; axby - aybx}</span>
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<span>Объем
пирамиды равен: </span>
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<span>(AB{x1, y1, z1} ; AC{x2, y2, z2} ; AD{x3, y3, z3})= x3·a1+y3·a2+z3·a3 </span></span></span></span><span><span>
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x y z
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AB*AC= -10 15
-5. </span></span></span><span>
V = (1/6)
*
140 = 140/6 = 70/3 </span>≈ <span>23,333333 куб.ед. Площадь грани ВСД: </span><span>
BCD
[BC ; BD]= (1/2)</span>√(8² + 12² + 24²) = (1/2)√784 =<span> <span>14 кв.ед. </span></span><span>Высота, опущенную из вершины А, равна: </span><span>
<span>H=3V/S = (3*(70/3))/14 = 5.</span></span>