Question

If $A(1, 1, 1), B(0, λ, 0), C(λ + 1, 0, 1), D(2, -2, 2)$ are co-planer then $\sum (\lambda_i + 2)^2$ is equal to

• A. $\frac{80}{3}$
• B. $\frac{320}{9}$
• C. $\frac{160}{9}$
• D. $\frac{160}{3}$

Answer 1

Answer: (C)

$\frac{160}{9}$

Answer 2

[$\overrightarrow{AB}$ $\overrightarrow{AC}$ $\overrightarrow{AD}$]=0
⇒ λ = 2, $\frac{-2}{3}$
$\sum (\lambda_i + 2)^2$ = 16+$\frac{16}{9}$ = $\frac{160}{9}$

So, the correct answer is (C): $\frac {160}{9}$