Question

Assertion (A) : A null vector is a vector whose magnitude is zero and direction is arbitrary
Reason(R) : A null vector does not exist
(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true, but R is not the correct explanation of A.
(C) A is true but R is False.
(D) A is False but R is true.

Answer 1

Hint:
A vector is a geometric entity with a magnitude and a direction. A null vector is a vector with 0 length and an undetermined direction. Its components are all equal to 0. In addition to this, the null vector is also known as the zero vector.


Complete step by step solution:
A vector in space with a magnitude of zero and an unclear direction is known as a zero vector or a null vector. An example of a zero vector sign is $\vec{0}=(0,0,0)$in three dimensional space and we can also write it in two dimensional space i.e. $\vec{0}=(0,0)$.
A null vector has zero length and doesn’t point in any directions, hence each of its components is equal to 0. As the outcome of adding a zero vector to any other non-zero vector always equals the original non-zero vector, it is also known as the additive validity of the set of vectors.
In the given question considering what we discussed above, the assertion is true but the reason is false because a null vector does exist.
For example two equal vectors pointing opposite to each other forms a null vector with an arbitrary direction.
Therefore, the correct option is C.




Note:
A zero vector has no value and points in no particular direction. In vector algebra, a null vector is an additive identity. The product of a zero vector with some other vectors is always zero. To tackle these problems we need to have a proper understanding of the concept of vectors.