JEE Advanced 2022 Paper 2 Mathematics Q13

Mathematics

Problem

Let â=(3,1,−1),

\vec{b}

=(1,b₂,b₃) and

\vec{c}

=(c₁,c₂,c₃) be three vectors such that b₂b₃>0, â·

\vec{b}

=0 and [[0,−c₃,c₂],[c₃,0,−c₁],[−c₂,c₁,0]][1,b₂,b₃]ᵀ=[3−c₁,1−c₂,−1−c₃]ᵀ. Then, which of the following is/are TRUE?