If A → and B → are two vectors satisfying the relation A → · B → = | A → × B → | . Then the value of | A → - B → | will be:

A → · B → = | A → × B → | A B cosθ = A B sinθ ⇒ θ = 45 ° | A → - B → | = A 2 + B 2 - 2 A B cos 45 ° = A 2 + B 2 - 2 A B Hence option ( 4 ) .

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Physics - Vectors Question with Solution | TestHub

PhysicsVectorsAddition/SubtractionEasy2 minPYQ_2021

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If $\vec{A}$ and $\vec{B}$ are two vectors satisfying the relation $\vec{A} \cdot \vec{B} = | \vec{A} \times \vec{B} |$ . Then the value of $| \vec{A} - \vec{B} |$ will be:

Options:

Answer:

Solution:

$\vec{A} \cdot \vec{B} = | \vec{A} \times \vec{B} |$
$A B cosθ = A B sinθ \Rightarrow θ = 45 °$
$| \vec{A} - \vec{B} | = \sqrt{A^{2} + B^{2} - 2 A B \cos 45 °}$
$= \sqrt{A^{2} + B^{2} - \sqrt{2} A B}$
Hence option $(4) .$

Stream:JEESubject:PhysicsTopic:VectorsSubtopic:Addition/Subtraction

⏱ 2mℹ️ Source: PYQ_2021

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