Physics · Motion In A Plane · NEET
| Magnitude | Equal vectors: must be identical | Collinear vectors: can be different |
| Direction | Negative vector: exactly opposite | Null vector: none defined |
| Magnitude value | Unit vector: always 1 | Null vector: always 0 |
No. Parallel (collinear) vectors only need the same direction; their magnitudes can differ. Equal vectors need BOTH the same magnitude AND the same direction. So every equal pair is parallel, but not every parallel pair is equal. Example: a 5 N and a 10 N force pointing east are parallel but not equal.
Yes. A vector has no fixed starting point. If you shift a vector without turning it or changing its length, it stays the same vector. So two arrows drawn at different places are equal as long as their length (magnitude) and direction match. This is why we can freely slide vectors in the triangle and parallelogram laws.
No. i-hat, j-hat, k-hat are the special unit vectors along the axes, but ANY direction can have its own unit vector. For any vector A, the unit vector along it is A-hat = A / |A|. Its only job is to point in a direction; its magnitude is always 1 and it has no units.
A negative vector -A has the same magnitude as A but points the opposite way, so |-A| = |A|. A null vector 0 has zero magnitude and no defined direction. Adding a vector to its negative gives the null vector: A + (-A) = 0. Do not confuse 'negative' (reversed) with 'zero' (nothing).
Antiparallel vectors are one case of collinear vectors. Collinear means all vectors lie along the same line or parallel lines. If they point the same way they are parallel; if they point opposite ways they are antiparallel. Both are collinear because the angle between them is either 0 degrees or 180 degrees.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Null (zero) vector, unit vector, equal vectors, negative vectors, and collinear (parallel/antiparallel) vectors. These appear in Motion in a Plane and are the base for vector addition, dot product and cross product.
A unit vector is a vector whose magnitude is exactly 1. It has no dimensions and no units and is used only to point in a direction. For a vector A, its unit vector is A-hat = A / |A|.
A null (zero) vector has magnitude 0, written as 0 with |0| = 0. Because its length is zero, there is no direction to specify. It appears when you add a vector to its negative: A + (-A) = 0, or when you multiply any vector by the number zero.
When they have the same magnitude and the same direction, no matter where they are drawn. You can slide one over the other and they will match exactly.
Every vector operation in Motion in a Plane and Laws of Motion relies on these definitions. Equal and negative vectors set up subtraction, collinear vectors decide when the resultant is simply added or subtracted, and unit vectors let you resolve any vector into i, j, k components.
