JEE Main 2023 (Online) 25th January Evening ShiftQuestion 1
If the four points, whose position vectors are $3\hat i-4\hat j+2\hat k$, $\hat i+2\hat j-\hat k$, $-2\hat i-\hat j+3\hat k$ and $5\hat i-2\alpha\hat j+4\hat k$ are coplanar, then $\alpha$ is equal to :
Vector Algebra
Solution
Coplanar: $\begin{vmatrix}-2&6&-3\\-5&3&1\\2&4-2\alpha&2\end{vmatrix}=146-34\alpha=0\Rightarrow\alpha=\frac{73}{17}$.