1. Tardigrade
  2. Question
  3. Mathematics
  4. If three vectors 2i - j - k , i + 2j - 3k and 3i + λ j + 5k are coplanar, then the value of λ is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If three vectors $ 2i - j - k $ , $ i + 2j - 3k $ and $ 3i + \lambda j + 5k $ are coplanar, then the value of $ \lambda $ is

MHT CETMHT CET 2012

Solution:

Let $a = 2i - j - k $,
$ b = i +2j -3k $
and $c =3i +\lambda j + 5 k$
If these vectors are coplanar, then $[a \,b\, c] = 0 $
$\Rightarrow \begin{vmatrix}2&-1&-1\\ 1&2&-3\\ 3&\lambda&5\end{vmatrix}=0$
$\Rightarrow 2(10+3 \lambda)+(5+9)-(\lambda-6)=0$
$\Rightarrow 20+6 \lambda+14-\lambda+6=0$
$\Rightarrow 5 \lambda+40=0$
$\Rightarrow \lambda=-8$