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Консультация № 121424
03.02.2008, 12:54
0.00 руб.
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найти точку В и вектор АВ,если вектор АВ коллинеарен вектору а=(-4;3;-12),образует с осью OY острый угол и вектор АВ=26
Обсуждение
Неизвестный
05.02.2008, 17:13
общий
это ответ
Здравствуйте, Долгиленко Людмила!
Поскольку АВ коллинеарен вектору а=(-4;3;-12) => существует k, что AB = (-4k;3k;-12k).
Тогда |AB|² = 16k²+9k²+144k² = 169k² => |AB| = 13|k|
|AB| = 26 => |k| = 2
Т.к. вектор АВ образует с осью OY острый угол => его координата х положительна => -4k > 0 => k<0
=> k = -2
Итак, АВ (8, -6, 24)
Для того, чтобы найти т. В, требуются дополнительные данные.
Поскольку АВ коллинеарен вектору а=(-4;3;-12) => существует k, что AB = (-4k;3k;-12k).
Тогда |AB|² = 16k²+9k²+144k² = 169k² => |AB| = 13|k|
|AB| = 26 => |k| = 2
Т.к. вектор АВ образует с осью OY острый угол => его координата х положительна => -4k > 0 => k<0
=> k = -2
Итак, АВ (8, -6, 24)
Для того, чтобы найти т. В, требуются дополнительные данные.
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