\( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) are the position vectors of the points \( A \e... VIDEO
\( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) are the position vectors of the points \( A \equiv(x \), \( y, z) ; B \equiv(y,-2 z, 3 x) ; C \equiv(2 z, 3 x,-y) \) and \( D \equiv(1,-1,2) \) respectively. If \( |\vec{a}|=2 \sqrt{3} ;(\vec{a} \vec{b})=(\vec{a} \vec{c}) ;(\vec{a} \vec{d})=0 \) and
\( (\vec{a} \hat{j}) \) is negative, then find \( x, y, z \).
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