How do I start this vector field problem?

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Consider the tetrahedron $ABCD$ where the vertices $A , B , C$ and $D$ have the Cartesian coordinates:

$$A=(0,0,0), \quad B=(1,0,0), \quad C=(0,2,0) \quad \text{and} \quad D=(0,0,3)$$

Draw the tetrahedron

Confirm that the plane $BCD$ has the equation $6x+3y+2z=6$ making sure that $B,C$ and $D$ all satisfy the equation

Deduce that:

  1. $BC$ has equation $y=2-2x$.

  2. $DB$ has equation $z=3-3x$.

  3. $CD$ has equation $z=3-1.5y$.

Question: How do I draw the tetrahendron and how do I confirm the equation given hence, therefore, leading to work out $BC,DB,CD$ ?