JEE Main 2023 (Online) 6th April Evening ShiftQuestion 1
The sum of all values of $\alpha$, for which the points whose position vectors are $\hat{i}-2\hat{j}+3\hat{k}$, $2\hat{i}-3\hat{j}+4\hat{k}$, $(\alpha+1)\hat{i}+2\hat{k}$ and $9\hat{i}+(\alpha-8)\hat{j}+6\hat{k}$ are coplanar, is equal to
Vector Algebra
Solution
Coplanar: $\det[P_2-P_1,P_3-P_1,P_4-P_1]=0$ with rows $(1,-1,1)$, $(\alpha,2,-1)$, $(8,\alpha-6,3)$. Expansion gives $\alpha^2-2\alpha-8=0\Rightarrow\alpha=-2,4$. Sum $=2$. Option (B).