Question

Give an example for which →A·→B=→C·→B but →A ≠→C.

Answer 1

Explanation:

in an isoceles triangleABC

• let ac be the hypotenuse
• so wkt,AB=CB(because it is an isoceles triangle)
• ab is not equal to ac

Answer 2

An example for which →A·→B=→C·→B but →A ≠→C is as follows

Explanation:

It is to be proven that  

$\vec A . \vec B = \vec C.\vec B, but \vec A not equal to \vec C$

Let’s assume that to $\vec B.\vec A$ is perpendicular and $\vec B$$\vecB$ is along the direction of west.

Also, to $\vec C \vec A and \vec C \vec B$ is perpendicular and it is along the north and south directions.

 To $\vec B \vec A$ is perpendicular. Hence, the scalar or dot product is zero.

That is, $\vec A. \vec B = A.B cos\theta = 0$

To $\vec C ,\vec B$ is perpendicular. Hence, the scalar or dot product is zero.

That is,  

$\vec C.\vec B = \vec C. \vec B cos 90 = 0$

Therefore, $\vec A . \vec B = \vec C.\vec B, but \vec A not equal to \vec C$

Hence, it is proved.