Question Video: Understanding Vectors with Zero Magnitude | Nagwa Question Video: Understanding Vectors with Zero Magnitude | Nagwa

# Question Video: Understanding Vectors with Zero Magnitude Science • Third Year of Preparatory School

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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.

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### 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.

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