Q.If $\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta$ and $\vec{a} \times \vec{b} = |\vec{a}| |\vec{b}| \sin \theta \hat{n}$ , then $\hat{n}$ is

unit vector perpendicular to both a and b

unit vector in plane of a and b

zero vector

none

The correct solution involves applying the fundamental concept to derive the final value step by step...

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Q.If a⃗⋅b⃗=∣a⃗∣∣b⃗∣cos⁡θ\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \thetaa⋅b=∣a∣∣b∣cosθ and a⃗×b⃗=∣a⃗∣∣b⃗∣sin⁡θn^\vec{a} \times \vec{b} = |\vec{a}| |\vec{b}| \sin \theta \hat{n}a×b=∣a∣∣b∣sinθn^, then n^\hat{n}n^ is