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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue
mathsVector AlgebraProperties of Vectors

Properties of Magnitude of a Vector

In this topic, Properties of Magnitude of vectors are explained in detail.



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What is the magnitude of a null vector?

  • `0`
  • `0`
  • `1`

The answer is '`0`'.

Null vector is `vec 0 = 0i+0j+0k`. So the magnitude `|vec 0| = 0`.

Properties of magnitude of vectors :
 •  Magnitude of a null vector is `0`.

Magnitude of a Null vector: Null vector is `vec 0 = 0i+0j+0k`. The magnitude `|vec 0| = 0`

Given vector `vec p` What is the magnitude of negative of `vec p`??

  • `|vec p|`
  • `|vec p|`
  • `-|vec p|`

The answer is '`|vec p|`'. The negative of `vec p` is `-vec p = -p_x i - p_y j - p_z k ` and so
`|-vec p| `
`quad quad = sqrt((-p_x)^2+(-p_y)^2+(-p_z)^2)`
`quad quad = sqrt((p_x)^2+(p_y)^2+(p_z)^2)`
`quad quad = |vec p|`

.

 •  Magnitude of the negative of a vector equals magnitude of the vector.

Magnitude of negative vector: For a vector `vec p`, the magnitude of the negative `|-vec p| = |vec p|`

What is the magnitude of a proper vector?

  • `=0`
  • `!=0`
  • `!=0`

The answer is '`!=0`'.

By definition, a proper vector is not a null vector. So the magnitude of the vector is not zero.

 •  Magnitude of a proper vector is not zero and positive.

Magnitude of Proper Vector: For a proper vector `vec p`, the magnitude `|vec p| != 0` and `|vec p| > 0`

What is the magnitude of a unit vector?

  • `0`
  • `1`
  • `1`

The answer is '`1`'.

By definition, magnitude of an unit vector is 1.

 • Magnitude of an unit vector is 1.

Magnitude of a unit vector: For a unit vector `vec p`, `|vec p| =1`

                            
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