In this page, computing magnitude of a vector is explained in detail.

*click on the content to continue..*

What is the length of the `vec(OP)` in the figure?

- `3+4`
- `7`
- both the above
- `sqrt(3^2+4^2)`
- `sqrt(3^2+4^2)`

Answer is '`sqrt(3^2+4^2)`', which is computed using the formula to find hypotenuse of right angled triangles (Pythagoras theorem).

What is the length of the `vec(OP)` in the figure?

- This does not form any right angled triangles to calculate OP
- `sqrt(3.3^2+2.5^2)`
- `sqrt(3.3^2+2.5^2-3.1^2)`
- `sqrt(3.3^2+2.5^2+(-3.1)^2)`
- `sqrt(3.3^2+2.5^2+(-3.1)^2)`

Answer is '`sqrt(3.3^2+2.5^2+(-3.1)^2)'`.

How this is calculated?

How is the length of the vector `vec OP` calculated?

- length of `bar(ON)` is calculated using `bar(OM)` and `bar(MN)` as sides of a right angled triangle `OMN`
- length of `bar(OP)` is calculated using `bar(ON)` and `bar(NP)` as sides of a right angled triangle `ONP`
- both the above as two steps
- both the above as two steps

Answer is 'both the above'.

This uses Pythagoras Theorem in two steps.

A vector is defined as a quantity with magnitude and direction. If the direction information in removed, the magnitude of a vector is obtained. In this example, length of `bar(OP)` is the magnitude of the vector.

The magnitude of a vector `ai+bj+ck` is given by `sqrt(a^2+b^2+c^2)`

**Magnitude** of a vector is the 'amount' of the quantity without the direction information.

**Magnitude of a Vector: ** For a vector `vec p = ai+bj+ck` the magnitude is

`|vec p| = sqrt(a^2+b^2+c^2)`

Does the word 'magnitude' has any meaning?

- yes, it means size of something.
- of course, yes, it means size
- obviously it is both the above
- obviously it is both the above

Guess what, you are right.

*Solved Exercise Problem: *

A point P is given by the vector `2i+4j-2k`. What is the distance of the point from the origin?

- `sqrt(2^2+4^2+(-2)^2)`
- `sqrt(2^2+4^2+(-2)^2)`
- `sqrt(2^2+4^2-2^2)`
- `2+4-2`
- `2+4+2`

Answer is '`sqrt(2^2+4^2+(-2)^2)`'

*slide-show version coming soon*