Hình Học Không Gian

Question

Cho tứ diện

$\rm{ABCD.M,N}$ thỏa mãn :

$\rm{\overrightarrow{MA}= -2\overrightarrow{MB}}$

$\rm{\overrightarrow{ND}= -2\overrightarrow{NC}}$

$\rm{ I ,J ,K}$ thỏa mãn :

$\rm{\overrightarrow{IA} =k\cdot\overrightarrow{ID}}$

$\rm{\overrightarrow{JM} =k\cdot\overrightarrow{JN}}$

$\rm{\overrightarrow{KB} =k\cdot\overrightarrow{KC}}$

cmr

$\rm{I ,J ,K}$ thẳng hàng.

tran85295 · Answer 1 · 1/27/2017 2:08:42 AM

Ta có

$\rm \vec{AM}+\vec{DN}=\left(\vec{AI}+\vec{IJ}+\vec{JM}\right)+\left ( \vec{DI}+\vec{IJ}+\vec{JNM} \right )\\ \Rightarrow 2\vec{IJ}=\left ( \vec{AM}+\vec{DN} \right )-\left ( \vec{AI}+\vec{DI} \right )-\left ( \vec{JM}+\vec{JN} \right ) \\ = \left ( \vec{AM}+\vec{DN} \right )+(k+1)\vec{ID}-(k+1)\vec{JN}(1)$

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