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Vector — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsVector1 Mark
Question
Assertion : If $\vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{C}$, then $\vec{A}$ may not always be equal to $\vec{C}$
Reason : The dot product of two vectors involves cosine of the angle between the two vectors.
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Answer

$ \vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{C} \Rightarrow A B \cos \theta_1=B C \cos \theta_2 $
$ \therefore A=C, \text { only when } \theta_1=\theta_2$
So when angle between $\vec{A}$ and $\vec{B}$ is equal to angle between $\vec{B}$ and $\vec{C}$ only then $\vec{A}$ equal to $\vec{C}$

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