# Give an Example for Which → a ⋅ → B = → C ⋅ → B but → a ≠ → C . - Physics

Sum

Give an example for which $\vec{A} \cdot \vec{B} = \vec{C} \cdot \vec{B} \text{ but } \vec{A} \neq \vec{C}$.

#### Solution

To prove:
$\vec{A} \cdot \vec{B} = \vec{C} \cdot \vec{B,} \text{ but } \vec{A} \neq \vec{C}$
Suppose that
$\vec{A}$  is perpendicular to
$\vec{B};\vec{B}$ is along the west direction.
Also, $\vec{B}$ is perpendicular to vecC ; vecA
$\vec{C}$ are along the south and north directions, respectively.

vecA is perpendicular to $\vec{B}$, so there dot or scalar product is zero.
i.e .,

$\vec{A} \cdot \vec{B} = \left| \vec{A} \right|\left| \vec{B} \right|\cos\theta = \left| \vec{A} \right|\left| \vec{B} \right|\cos90^\circ= 0$
$\vec{B}$ is perpendicular to $\vec{C}$,  so there dot or scalar product is zero.
i.e., $\vec{C} \cdot \vec{B} = \left| \vec{C} \right|\left| \vec{B} \right|cos\theta = \left| \vec{C} \right|\left| \vec{B} \right|cos90\ = 0$
$\therefore \vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{C,} but \vec{A} \neq \vec{C}$

Hence, proved.

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 2 Physics and Mathematics
Exercise | Q 19 | Page 29