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Thought-Process to Discover Knowledge

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mathsVector AlgebraVectors and Coordinate Geometry

Position Vector of a Point

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.position vector of a point 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 definition Position vector of a point `P (a,b,c)` is

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

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`'.

slide-show version coming soon