Question

What are equal vectors?

• A. Two or more vectors are said to be equal if they are parallel to the same line, irrespective of their magnitudes and directions.
• B. Two vectors and are said to be equal, if they have the same magnitude and direction regardless of the positions of their initial points .
• C. Two vectors and are said to be equal, if they have the same magnitude and direction, Also same positions of their initial points .
• D. None of the above

Answer 1

Answer: (B), (C)

Two vectors and are said to be equal, if they have the same magnitude and direction, Also same positions of their initial points .
Two vectors and are said to be equal, if they have the same magnitude and direction regardless of the positions of their initial points .

according to the definition of equal vector

1)the magnitude of both vectors should be equal

$\left|\overrightarrow{a}\right|=\left|\overrightarrow{b}\right|$

2)the direction should be same

$\overrightarrow{OA}=\overrightarrow{OB}$

Hence option B is correct

Equal vectors are defined as two vectors having same magnitude and direction. They may or may not have same initial point

So if the initial point is same then they will also equal vector if both vectors satisfying condition of equal vector.

Note: It is a definition and has no proof