Physics · Motion In A Plane · NEET
It is a genuine vector, not a scalar. We write it in bold as 0 (with an arrow) to show it belongs to the vector family. The difference from the scalar 0 is that a null vector obeys vector rules: you can add it to another vector (a + 0 = a) and multiply it by a scalar. It just happens to have magnitude zero.
No fixed direction can be assigned to it. NCERT states directly that since the magnitude of a null vector is zero, its direction cannot be specified. This is different from every other vector, which always has a definite direction. For NEET, remember: null vector = zero magnitude AND undefined (arbitrary) direction.
When they are equal in magnitude but opposite in direction. If you add a and -a, the two arrows cancel: a + (-a) = 0. In physics this happens when forces or displacements balance out. Example: walk 5 m east then 5 m west - your displacement vector is the null vector, because start and end points are the same.
They are opposites in magnitude. A null vector has magnitude 0 and no direction. A unit vector has magnitude exactly 1 and is used only to point in a direction. So do not mix them up: null vector shows 'nothing added,' unit vector shows 'pure direction.'
Yes. If you multiply any vector a by the scalar 0, you get the null vector: 0 a = 0. Also, multiplying the null vector by any scalar still gives the null vector: lambda 0 = 0. These are the standard properties you must memorise for the exam.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
A null vector is a vector with magnitude zero and no definite direction. It is written as 0 and results from adding equal and opposite vectors, like a + (-a) = 0.
Three NCERT properties: a + 0 = a (adding it changes nothing), lambda 0 = 0 (any scalar times null is null), and 0 a = 0 (zero times any vector is null). Its magnitude |0| = 0.
Because its magnitude is zero. NCERT states that since the magnitude of a null vector is zero, its direction cannot be specified. Its direction is treated as arbitrary or undefined.
Yes. a - a = 0. Subtracting a vector from itself always gives the null vector, since both magnitude and direction cancel completely.
Yes, as a concept. It appears in questions on balanced forces, zero resultant, and closed polygons of vectors. Knowing that a null vector is still a vector helps you avoid common trap options.
