JEE Main & Advanced
Mathematics
Vector Algebra
Question Bank
Numerical Value Type Questions - Vector Algebra
question_answer
Let \[\alpha \in R\] and the three vectors \[\overset{\to }{\mathop{a}}\,=\alpha \hat{i}+\hat{j}+3\hat{k},\] \[\overset{\to }{\mathop{b}}\,=2\hat{i}+\hat{j}-\alpha \hat{k}\] and \[\overset{\to }{\mathop{c}}\,=\alpha \hat{i}-2\hat{j}+3\hat{k}.\] Then, the number of elements in the set S=( \[\alpha :\overset{\to }{\mathop{a}}\,,\,\,\vec{b}\] and \[\overset{\to }{\mathop{c}}\,\] are coplanar) is