Giải thích các bước giải:
Em tự vẽ hình nhé
\(\begin{array}{l}
\overrightarrow {MN} .\overrightarrow {MP} \\
= \left( {\overrightarrow {MB} + \overrightarrow {BA} + \overrightarrow {AN} } \right)\left( {\overrightarrow {MC} + \overrightarrow {CD} + \overrightarrow {DP} } \right)\\
= \overrightarrow {MB} .\overrightarrow {MC} + \overrightarrow {MB} .\overrightarrow {CD} + \overrightarrow {MB} .\overrightarrow {DP} \\
+ \overrightarrow {BA} .\overrightarrow {MC} + \overrightarrow {BA} .\overrightarrow {CD} + \overrightarrow {BA} .\overrightarrow {DP} \\
+ \overrightarrow {AN} .\overrightarrow {MC} + \overrightarrow {AN} .\overrightarrow {CD} + \overrightarrow {AN} .\overrightarrow {DP} \\
= \dfrac{a}{2}.\dfrac{a}{2} + \dfrac{a}{2}.a.\cos {60^0} + \dfrac{a}{2}.\dfrac{{a\sqrt 3 }}{3}\cos {30^0}\\
+ \dfrac{a}{2}.a.\cos {60^0} + a.a - a.\dfrac{{a\sqrt 3 }}{3}.\cos {30^0}\\
+ \dfrac{a}{4}.\dfrac{a}{2}\cos {60^0} - \dfrac{a}{4}.a.\cos {60^0} + 0\\
= \left( {\dfrac{{17}}{{16}} - \dfrac{{\sqrt 3 }}{{12}}} \right){a^2}
\end{array}\)
