a=i+j+k, ,b=2i-4k, ,c=i+ ,j+3k are coplanar, then the value of is - Vidyadip

MCQ

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

A
$5/2$
B
$3/5$
C
$7/3$
✓
None of these

✓

Answer

Correct option: D.

None of these

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

$\therefore [a b c]$ $ \Rightarrow \,\,\,\left| {\,\begin{array}{*{20}{c}}1&1&1\\2&0&{ - 4}\\1&\lambda &3\end{array}\,} \right|\, = 0$

$ \Rightarrow 4\lambda - \left( {6 + 4} \right) + 2\lambda = 0$

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

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