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**mechaniac** determine the constant $\displaystyle \beta $ so that the points $\displaystyle A=(0,-8,-3),B=(3,\beta,1),C=(-1,0,0),D=(2,1,1)$ is in a plane.

I started to put up two vectors with the points A,B,C:

$\displaystyle \bar{AB}=(3,\beta+8,4)$

$\displaystyle \bar{AC}=(-1,8,3)$

now i thought that if i choose $\displaystyle \beta$ so that the two vectors makes a plane, i can get the equation for the plane and proof that the point D is in the plane.

How do i choose $\displaystyle \beta$ so the vectors makes a plane?

Thanks!