Physics · Motion In A Plane · NEET
No. Same magnitude is only HALF the rule. NCERT says two vectors A and B are equal if, and only if, they have the same magnitude AND the same direction. A vector of 5 N pointing east is NOT equal to a vector of 5 N pointing north, even though both have magnitude 5 N. Direction must match too.
No. Position does not matter for equality. In our NEET study, vectors are free vectors, so moving a vector parallel to itself leaves it unchanged. Two arrows in different parts of the page can still be equal if their length and direction are the same. This is why a displacement of 10 m north is the same vector wherever you draw it.
Use the NCERT shift-parallel test. Shift vector B parallel to itself (keep its direction fixed) until its tail meets the tail of vector A. If the tip (head) of B now lands exactly on the tip of A, the two vectors are equal, so A = B. If the tips do NOT coincide, they are not equal even if the lengths look close.
Yes. Parallel vectors point along the same line, but they can have different magnitudes, so they are not equal. Also, two vectors can be anti-parallel (same line, opposite direction, like A and -A): same magnitude but opposite direction still means NOT equal. Equal needs BOTH same magnitude and same direction, not just the same line.
No, and NEET loves this trap. Equal magnitude means only the numbers (lengths) are the same. Equal vectors means magnitude AND direction are both the same. Every pair of equal vectors has equal magnitude, but not every pair of equal-magnitude vectors is equal, because their directions can differ.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Two vectors A and B are equal if, and only if, they have the same magnitude and the same direction. This is the NCERT Class 11 definition (Section 3.2.2). Both conditions must hold together.
No. For free vectors used in NEET mechanics, shifting a vector parallel to itself does not change it. So two vectors drawn at different places can still be equal if their magnitude and direction match.
If two vectors are equal, all their corresponding rectangular components are equal. So Ax = Bx and Ay = By (and Az = Bz in 3D). Comparing components is the fastest way to check equality in NEET numerical problems.
No. A and -A (the negative vector) have the same magnitude but exactly opposite directions. Since the directions differ, they are not equal. They are called negative vectors of each other.
It is the base rule for vector addition, resolution, and equilibrium. In equilibrium and component problems you often set two vectors equal, which means matching both magnitude and direction (or matching each component). Getting this rule right prevents silly errors in Motion in a Plane and Laws of Motion questions.
