MCQ 11 Mark
Assertion (A): If $\vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{C}$, then $\vec{A}$ may not always be equal to $\vec{C}$.
Reason (R): The dot product of two vectors involves cosine of the angle between the two vectors.
Reason (R): The dot product of two vectors involves cosine of the angle between the two vectors.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer
View full question & answer→Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
Explanation: As $\vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{C} \Rightarrow AB \cos \theta_1= BC \cos \theta_2$
$\Rightarrow A = C$, 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 $\vec{C}$.
Explanation: As $\vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{C} \Rightarrow AB \cos \theta_1= BC \cos \theta_2$
$\Rightarrow A = C$, 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 $\vec{C}$.