If the vectors $\hat{\imath}+\hat{\jmath}+\hat{k}, \hat{\imath}-\hat{\jmath}+\hat{k}$ and $2 \hat{\imath}+3…
If the vectors $\hat{\imath}+\hat{\jmath}+\hat{k}, \hat{\imath}-\hat{\jmath}+\hat{k}$ and $2 \hat{\imath}+3 \hat{\jmath}+m \hat{k}$ are coplanar, then $m=$
3
-2
2
-3
Solution
Since given vectors are coplanar, we write
$\begin{array}{l}
\left|\begin{array}{ccc}
1 & 1 & 1 \\
1 & -1 & 1 \\
2 & 3 & \mathrm{~m}
\end{array}\right|=0 \\
\therefore(-\mathrm{m}-3)-(\mathrm{m}-2)+(3+2)=0 \Rightarrow 2 \mathrm{~m}=4 \Rightarrow \mathrm{m}=2
\end{array}$