Question

If (2, 3, 9), (5, 2, 1), (1, λ, 8) and (λ, 2, 3) are coplanar, then the product of all possible values of λ is :

• A. $\frac{21}{2}$
• B. $\frac{59}{8}$
• C. $\frac{57}{8}$
• D. $\frac{95}{8}$

Answer 1

Answer: (D)

$\frac{95}{8}$

Answer 2

Since (2, 3, 9), (5, 2, 1), (1, λ, 8) and (λ, 2, 3) are coplanar.
Therefore $\begin{vmatrix}λ-2&-1&-6\\\\-1&λ-3&-1\\\3&-1&-8\end{vmatrix}=0$

∴8λ$^2$–67λ+95=0
∴Product of all values of λ=$\frac{95}{8}$

So, the correct option is (D): $\frac{95}{8}$