We have, a and b are orthogonal vectors ∴‌‌a⋅b=0
⇒−tan‌θ+tan2θ+‌
3
√sin‌
θ
2
(−2√sin‌
θ
2
)=0
⇒−tan‌θ+tan2θ−6=0 ⇒tan2θ−tan‌θ−6=0 ⇒(tan‌θ−3)(tan‌θ+2)=0 ⇒tan‌θ=3,−2 Now, c makes an obtuse angle with X -axis ∴sin‌2‌θ<0 ⇒‌