Giải thích các bước giải:
a,
Ta có:
\(\overrightarrow {AC} \left( {\overrightarrow {AB} + \overrightarrow {AD} } \right) = \overrightarrow {AC} \left( {\overrightarrow {AB} + \overrightarrow {BC} } \right) = \overrightarrow {AC} .\overrightarrow {AC} = A{C^2} = 2A{B^2} = 2{a^2}\)
b,
\(\begin{array}{l}
\left( {\overrightarrow {AB} + \overrightarrow {AD} } \right)\left( {\overrightarrow {BD} + \overrightarrow {BC} } \right)\\
= \left( {\overrightarrow {AB} + \overrightarrow {BC} } \right).\left( {\overrightarrow {BD} + \overrightarrow {BC} } \right)\\
= \overrightarrow {AC} .\left( {\overrightarrow {BD} + \overrightarrow {BC} } \right)\\
= \overrightarrow {AC} .\overrightarrow {BD} + \overrightarrow {AC} .\overrightarrow {BC} \\
= \overrightarrow 0 + \overrightarrow {AC} .\overrightarrow {BC} \,\,\,\,\,\left( {do\,\,AC \bot BD} \right)\\
= \overrightarrow {AC} .\overrightarrow {BC} \\
= \left( {\overrightarrow {AB} + \overrightarrow {BC} } \right).\overrightarrow {BC} \\
= \overrightarrow {AB} .\overrightarrow {BC} + {\overrightarrow {BC} ^2}\\
= B{C^2}\,\,\,\,\,\,\left( {do\,\,\,\,AB \bot BC} \right) = {a^2}
\end{array}\)
