Question

If the four points $\left(3, -2 , -1\right), \left(2, 3, -4\right)$, $\left(-1, 1, 2\right)$ and $\left(4, 5, \lambda\right)$ are coplanar then $\lambda$ is equal to

• A. 0
• B. $- \frac{17}{146}$
• C. $- \frac{146}{17}$
• D. none of these.

Answer 1

Answer: (C)

$- \frac{146}{17}$

Answer 2

Let the four points be A, B, C and D respectively, t hen these are coplanar if $\overrightarrow{AB} \, \overrightarrow{AC} , \overrightarrow{AD}$ are coplanar, i.e. if $\left[\overrightarrow{AB } \overrightarrow{AC } \overrightarrow{AD }\right] = 0 ,$ i.e. if $\begin{vmatrix}-1&5&-3\\\ -4&3&3\\\ 1&7&\lambda+1\end{vmatrix}= 0$