If two vectors A → and B → having equal magnitude R are inclined at an angle θ , then

The magnitude of resultant vector A → + B → is given by, R ' = A 2 + B 2 + 2 A B cos θ Here A = B = R Then R ' = R 2 + R 2 + 2 R 2 cos θ = R 2 1 + cos θ = 2 R 2 cos 2 θ 2 = 2 R cos θ 2

Physics - Vectors Question with Solution | TestHub

PhysicsVectorsAddition/SubtractionEasy2 minPYQ_2024

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If two vectors $\vec{A}$ and $\vec{B}$ having equal magnitude $R$ are inclined at an angle $θ$ , then

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Answer:

Solution:

The magnitude of resultant vector $\vec{A} + \vec{B}$ is given by,

$R' = \sqrt{A^{2} + B^{2} + 2 A B \cos θ}$

Here $A = B = R$

Then $R' = \sqrt{R^{2} + R^{2} + 2 R^{2} \cos θ}$

$= R \sqrt{2} \sqrt{1 + \cos θ}$

$= \sqrt{2} R \sqrt{2 \cos^{2} \frac{θ}{2}}$

$= 2 R \cos \frac{θ}{2}$

Stream:JEESubject:PhysicsTopic:VectorsSubtopic:Addition/Subtraction

⏱ 2mℹ️ Source: PYQ_2024

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