Question

The points A(4,5,1), B(0,-1,-1), C(3,9,4) and D(-4,4,4) are

• A. Collinear
• B. Coplanar
• C. Non- coplanar
• D. Non- Collinear and non-coplanar

Answer 1

The correct option is B Coplanar

$AB\equiv (-4,-6,-2);AC\equiv (-1,4,3);AD\equiv (-8,-1,3)$
Points A, B, C, D are coplanar, if $[\overrightarrow{AB},\overrightarrow{AC},\overrightarrow{AD}]=0$
$\Rightarrow \left|\begin{array}{ccc}-4& -6& -2\\ -1& 4& 3\\ -8& -1& 3\end{array}\right|=0$
also we can observe A,B,C and D are not collinear