Cho A(1;2;5),B(1;0;2),C(4;7;−1),D(4;1;a). Để 4 điểm A,B,C,D đồng phẳng thì aa bằng:

Có

\(\left\{ {\begin{array}{*{20}{c}}{\overrightarrow {AB} = (1 - 1;0 - 2;2 - 5) = (0; - 2; - 3)}\\{\overrightarrow {AC} = (4 - 1;7 - 2; - 1 - 5) = (3;5; - 6)}\\{\overrightarrow {AD} = (4 - 1;1 - 2;a - 5) = (3; - 1;a - 5)}\end{array}} \right.\)

\(\left[ {\overrightarrow {AB} ,\overrightarrow {AC} } \right] = \left( {\left| {\begin{array}{*{20}{c}}{ - 2}&{ - 3}\\5&{ - 6}\end{array}} \right|;\left| {\begin{array}{*{20}{c}}{ - 3}&0\\{ - 6}&3\end{array}} \right|;\left| {\begin{array}{*{20}{c}}0&{ - 2}\\3&5\end{array}} \right|} \right) = (27; - 9;6)\)

\( \Rightarrow \left[ {\overrightarrow {AB} ,\overrightarrow {AC} } \right].\overrightarrow {AD} = (27; - 9;6).(3; - 1;a - 5) = 60 + 6a\)

\[A,B,C,D\]đồng phẳng khi\[\left[ {\overrightarrow {AB} ,\overrightarrow {AC} } \right].\overrightarrow {AD} = 0 \Leftrightarrow 60 + 6a = 0 \Leftrightarrow a = - 10\]

Đáp án cần chọn là: A