True or Flase
$$ {\vec{0}}=0$$
$$ \mathbf {0}=0$$

Question

True or Flase
$$  {\vec{0}}=0$$ 
$$ \mathbf {0}=0$$

unklerhaukus · Answer

where $$  {\vec{0}}$$ denotes the null (zero) vector


&

$$ \mathbf {0}$$ denotes the zero matrix

mani_jha · Answer

What I can say about the first one is that a zero vector doesn't have any well specified direction.(That's what I learned in Physics)
So, you can only say that the magnitude of a zero vector is zero. Since you can't specify its direction, it shouldn't be written in the vector form.
So is the first one false?

unklerhaukus · Answer

so the zero vector is not a vector?

mani_jha · Answer

It is somewhat, but it doesn't have a well-defined direction. Suppose I apply some force on an object, and you apply an equal force from the opposite direction. Now, If I ask you what is the direction of the net force on the body, will you able to answer? No one can, because the forces cancel each other and it isn't possible to say in which direction the resultant zero vector acts.
Zero vector is a vector, with magnitude zero but without a well-specified direction.
(The number zero creates so many confusions, that it is often known as the 'hero' of mathematics!)