Ward Stewart
10/02/2023 · Senior High School
6. Дан куб \( \mathrm{ABCDA}_{1} \mathrm{~B}_{1} \mathrm{C}_{1} \mathrm{D}_{1} \), ребро которого равно 1 cm . На диагонали \( \mathrm{A}_{1} \mathrm{~B} \) его грани отметили точку K так, что \( \mathrm{A}_{1} \mathrm{~K}: \mathrm{KB}=4: 3 \). 1) Выразите вектор \( \overrightarrow{C_{1} K} \) через векторы \( \overrightarrow{C_{1} B_{1}}, \overrightarrow{C_{1} D_{1}} \) и \( \overrightarrow{C_{1} C} \). 2) Найдите модуль вектора \( \overrightarrow{C_{1} K} \).
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Quick Answer
1) Вектор \( \overrightarrow{C_1K} \) можно выразить как:
\[
\overrightarrow{C_1K} = -\frac{3}{7} \cdot \overrightarrow{C_1D_1} - 1 \cdot \overrightarrow{C_1B_1} - \frac{4}{7} \cdot \overrightarrow{C_1C}
\]
2) Модуль вектора \( \overrightarrow{C_1K} \) равен:
\[
|\overrightarrow{C_1K}| = \frac{\sqrt{74}}{7}
\]
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