Let the vectors $\vec a =\hat i-3\hat j+2\hat k,\vec b=2\hat i+\hat j-\hat k$ and $\vec c=3\hat i+5\hat j-2λ\hat k$ be coplanar. Then $λ$. is equal to

2

All given vectors are coplanar.

$[\vec a\,\,\vec b\,\,\vec c]=0$

$\begin{vmatrix}1&-3&2\\2&1&-1\\3&5&-2λ\end{vmatrix}=0$

Applying $R_2→R_2-2R_1,R_3→R_3-R_2-R_1$

$\begin{vmatrix}1&-3&2\\0&7&-5\\0&7&-2λ-1\end{vmatrix}=0$

If two row are equal than determinant = 0

on comparing $R_2$ and $R_3$

$-2λ-1=-5⇒2λ=4⇒λ=2$