Question

If the points $A(2,1,-1)$, $B(0,-1,0)$, $C(4,0,4)$ and $D(2,0,x)$ are coplanar, then $x=$

• A. $2$
• B. $1$
• C. $4$
• D. $3$

Hint:

Coplanarity of points in 3D is checked using the determinant condition.

Answer 1

The Correct Option is B

Step 1: Using the coplanarity condition.
Four points are coplanar if the determinant formed by their coordinates is zero.
Step 2: Forming the determinant.
\[ \begin{vmatrix} 2 & 1 & -1 & 1\\ 0 & -1 & 0 & 1\\ 4 & 0 & 4 & 1\\ 2 & 0 & x & 1 \end{vmatrix}=0 \]
Step 3: Evaluating the determinant.
Simplifying, we obtain \[ x-1=0 \Rightarrow x=1 \]
Step 4: Conclusion.
The value of $x$ is $1$.