Statement I : If θ be the angle between A→ and B→, then $$tan$$θ $$=$$ A→ ×B→A→.B→Statement II : A→ ×B→ is perpendicular to A→.B→

Correct option is 4If both statement I and statement II are false.

Questions

Statement I : If $θ be the angle between \vec{A} and \vec{B}, then tanθ = \frac{\vec{A} \times \vec{B}}{\vec{A} . \vec{B}}$
Statement II : $\vec{A} \times \vec{B} is perpendicular to \vec{A} . \vec{B}$

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If both statement I and statement II are true and statement II is the correct explanation of statement I.

If both statement I and statement II are true but statement II is not the correct explanation of statement I.

If statement I is true but statement II is false.

If both statement I and statement II are false.

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detailed solution

Correct option is D

A→ ×B→A→.B→ = ABsinθn^ABcosθ =tanθn^where n^ is unit vector perpendicular to both A→ and B→.However |A→×B→|A→.B→ = tanθ

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Statement I : If θ be the angle between A→ and B→, then tanθ = A→ ×B→A→.B→Statement II : A→ ×B→ is perpendicular to A→.B→

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Statement I : If $θ be the angle between \vec{A} and \vec{B}, then tanθ = \frac{\vec{A} \times \vec{B}}{\vec{A} . \vec{B}}$
Statement II : $\vec{A} \times \vec{B} is perpendicular to \vec{A} . \vec{B}$