Question

$a = i + j + k,\mathbf{b} = 2i - 4k,c = i + \lambda j + 3k$ are coplanar, then the value of $\lambda$ is

• A. 5/2
• B. 3/5
• C. 7/3
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

$\because a = i + j + k$,$b = 2i - 4k,c = i + \lambda j + 3k$are coplanar.

∴$\lbrack abc\rbrack = 0 \Rightarrow \left| \begin{matrix} 1 & 1 & 1 \\ 2 & 0 & - 4 \\ 1 & \lambda & 3 \end{matrix} \right| = 0$

$\Rightarrow 4\lambda - (6 + 4) + 2\lambda = 0$

⇒ $6\lambda = 10 \Rightarrow \lambda = \frac{5}{3}$.