Are the four points $A(1, -1, 1), B(-1, 1, 1), C(1, 1, 1), D(2, -3, 4)$ coplanar?
AYes — they all lie in the plane $z = 1$.
BNo — point $D$ has $z = 4$, breaking the common plane.
CYes — all four lie on the line $y = -x$.
DCannot be determined from given data.
Answer & Solution
Correct answer: B. No — point $D$ has $z = 4$, breaking the common plane.
$A, B, C$ all have $z = 1$, so they lie in the plane $z = 1$. $D = (2, -3, 4)$ has $z = 4 \ne 1$, so $D$ does **not** lie in that plane. The four points are not coplanar. (For general coplanarity, check that $\overrightarrow{AD}$ is a linear combination of $\overrightarrow{AB}, \overrightarrow{AC}$.)
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