In this page, you will learn about position vector of a point. This concept connects vector algebra and coordinate geometry.

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Consider a point `P` in 3D coordinate system as shown in figure. What describes the point `P`?

- `(a,b,c)`
- `ai+bj+ck`
- `vec(OP)`
- all the above
- all the above

Answer is 'all the above'. It is understood as

`***` in 3D coordinates it is `(a,b,c)`

`***` as a vector representation `ai+bj+ck`

`***` as the vector `vec(OP)`

What does the word 'position' mean?

- place; location
- place; location
- positive; desirable

Answer is 'place; location'.

Given a point `P (a,b,c)` as shown in figure. Position vector of a point `P (a,b,c)` is

`vec(OP)=ai+bj+ck`

**Position Vector of a Point** is the vector between origin and the point.

**Position Vector: ** For a point `P (a,b,c)` the position vector is

`vec(OP)=ai+bj+ck`.

*Solved Exercise Problem: *

What is the position vector of point `(2,-3/4)`?

- `2i-3j+4k`
- `2i-3/4j`
- `2i-3/4j`
- `2i`
- `-3/4j`

Answer is '`2i-3/4j`'.

*Solved Exercise Problem: *

Given the vector `vec(OP) = 3i-1.4j+2.5k`, if `O` is the origin, what is the coordinate position of point `P`?

- `3-1.4+2.5`
- `(3,-1.4,2.5)`
- `(3,-1.4,2.5)`
- `(0,0,0)`
- `sqrt(3^2+1.4^2+2.5^2)`

Answer is '`(3,-1.4,2.5)`'

*Solved Exercise Problem: *

What is the position vector of point `(0,-2.1,3.4)`?

- `i-2.1j+3.4k`
- `-2i+3.4k`
- `-2i+3.4k`
- `-2.1j+3.4k`
- `-2.1j, 3.4k`

Answer is '`-2.1j+3.4k`'.

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