Which of the following is true?
- ATwo vectors having same magnitude are collinear
- BTwo collinear vectors are always equal in magnitude
- CTwo collinear vectors having the same magnitude are equal
- Dand are collinear
Solution & Step-by-step Explanation
To determine the truth of the statements, we analyze the definition of collinearity:Collinear Vectors: Vectors are collinear if they are parallel to the same line, regardless of their magnitudes or directions.Option A: Having the same magnitude does not imply being parallel. Two vectors can have magnitude but point in perpendicular directions. (False)Option B: Collinear vectors can have different magnitudes. (False)Option C: Two collinear vectors with the same magnitude could point in opposite directions (antiparallel), making them unequal (one is the negative of the other). (False)Option D: and are parallel to the same line (they are opposite in direction), thus they are collinear by definition. (True)