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|`

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• 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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