Vectors

Vectors

Both direction and magnitude are used as the basis for defining vector quantities. A vector that has zero magnitudes still has direction. When expressed in a drawing, a vector with a zero magnitude is shown by an arrow of zero length, which is impossible to draw (Danielson, 2018). Notably, this often prompts thinking that such a vector has no direction. However, this is not the case, considering that a vector quantity is defined by direction and magnitude. A vector with a magnitude of zero has a similar effect in the direction in which it acts compared to the direction in which it does not act. For example, a box being pushed by two equal forces from opposite directions will remain stationary. The box will appear stationary because the two equal forces will cancel each other, and the total force on the box will be zero net. Essentially, this forms a basis for the decision that specifying the direction for a vector with zero magnitudes is unnecessary.

Specifying the direction for a vector with zero magnitudes is not necessary because the direction is arbitral. It is referred to as a null vector because its magnitude is zero. A null vector does not exist, and it is hard to determine the particular direction of such a vector. However, since the magnitude is known to be zero, there is no need to mention the direction. The direction of such a vector is orthogonal and has a particular direction. It can be said that the direction of a vector with zero magnitudes in every direction is hard to specify and, thus, unnecessary.

Reference

Danielson, D. A. (2018). Vectors and tensors in engineering and physics. CRC Press.

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A vector has zero magnitudes. Is it necessary to specify its direction? Explain.