NIMCET 2023 — Mathematics PYQ

(a)
Fundamentally this question is wrong because sum of two vectors can not be equal to scalar.
But if we have solve this question.
$$|2\vec{a}+\vec{b}{|}^2=9$$
$$<br>\Rightarrow 4|\vec{a}{|}^2+|\vec{b}{|}^2+4\vec{a}\cdot \vec{b}=9$$
$$\Rightarrow \vec{a}\cdot \vec{b}=1$$
$$<br>\Rightarrow |\vec{a}|\cdot |\vec{b}|\cos \theta =1$$
$$\Rightarrow \cos \theta =1$$
$$<br>\Rightarrow \theta =0$$