question_answer

Let \[\alpha \in R\]and the three vectors \[\vec{a}=\alpha \hat{i}+\hat{j}+3\hat{k},\]             \[\vec{b}=2\hat{i}+\hat{j}-\alpha \hat{k}\] and  \[\vec{c}=\alpha \hat{i}-2\hat{j}+3\hat{k}.\]Then the set \[S=\{\alpha :\vec{a},\vec{b}\]and\[\vec{c}\]are coplanar\[\}\] [JEE Main 12-4-2019 Afternoon]

A) is singleton

B) Contains exactly two numbers only one of which is positive

C) Contains exactly two positive numbers

D) is empty