Which of the following statements are correct?
(A) Two vectors having the same magnitude are equal
(B) The zero vector may be regarded as having any direction
(C) Two or more vectors having the same initial point are called coinitial vectors
(D) Collinear vectors always have the same direction
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B) and (C) only
Two vectors are equal when they have the same magnitude and the same direction. The zero vector has zero magnitude, so no definite direction can be assigned to it; it may be regarded as having any direction. Vectors are collinear when they are parallel to the same line, whatever their magnitudes and directions.
So equality needs the same magnitude and the same direction, the zero vector may take any direction, coinitial vectors share the initial point, and collinear vectors can point in opposite directions.
Checking the statements
(A) Two vectors having the same magnitude are equal — Incorrect. \(\hat{\imath}\) and \(-\hat{\imath}\) both have magnitude 1 but are not equal.
(B) The zero vector may be regarded as having any direction — Correct. It has zero magnitude, so no single direction is fixed for it.
(C) Two or more vectors having the same initial point are called coinitial vectors — Correct. This is the definition of coinitial vectors.
(D) Collinear vectors always have the same direction — Incorrect. \(\hat{\imath}\) and \(-2\hat{\imath}\) are collinear but point in opposite directions.