Video Transcript
Which of the following most
correctly explains what happens if a vector has a magnitude of zero? (A) If the magnitude of the vector
is zero, it has the same effect in the direction in which it acts as in the
directions in which it does not act. (B) If the magnitude of the vector
is zero, it becomes a scalar.
We define a vector as a quantity
with both magnitude and direction. Recall that we can represent a
vector using an arrow. The length of the arrow represents
the magnitude of the vector, and the arrow points in the direction in which the
vector acts. In this question, we need to work
out what happens when a vector has a magnitude of zero.
A vector with a magnitude of zero
would be represented by an arrow of zero length. But this is impossible to draw. Because of this, we might think
that when a vector’s length is zero, it has no direction. However, this is not true. A vector quantity must always be
defined in terms of both its magnitude and its direction. Even if the magnitude of the vector
is zero, it still has to have a direction. This means that a vector of zero
magnitude can never be treated as a scalar. Therefore, we can rule out option
(B) from the question.
This leaves us with option (A). If the magnitude of the vector is
zero, it has the same effect in the direction in which it acts as in the directions
in which it does not act. This is a bit strange, so let’s
think of an example of a vector with zero magnitude. We’ll use a vector that we see
often in physics, force. The simple definition of force is a
push or a pull. So imagine two people on opposite
sides of a large box, pushing it with equal force in opposite directions. We’ll say that the person on the
left pushes with 10 newtons of force to the right and that the person on the right
pushes with 10 newtons of force to the left.
Note how we can’t describe a force
without indicating the direction in which it acts. Forces are vectors through and
through. Now think, what would happen to the
box? Would it begin to move? Well, nothing would happen. Because the people are applying
forces of equal magnitudes and opposite directions, the two force vectors
effectively cancel each other out. And there is zero net, or total,
force on the box.
So we have seen that when a force
of zero magnitude is applied to the box, the box doesn’t move. The people may be pushing it to the
left and right. But the box doesn’t move to the
left or the right or up or down or in any direction. Because the force has a magnitude
of zero, the effect of the force is the same in the direction in which it acts as in
the directions in which it does not act. This is true of any vector, and
thus option (A) is the correct answer to this question.
If a vector has a magnitude of
zero, the effect of the vector is the same in the direction in which it acts as in
the directions in which it does not act.
