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Vectors and Coordinate Geometry

Vectors and Coordinate Geometry

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Position Vector of a Point


 »  For a point `P(a,b,c)` the position vector is `vec(OP) = ai+bj+ck`

Position Vector of a Point

plain and simple summary

nub

plain and simple summary

nub

dummy

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

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simple steps to build the foundation

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


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Starting on learning "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.

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

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
  • 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
`vec(OP)=ai+bj+ck`

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Position Vector: For a point `P (a,b,c)` the position vector is
`vec(OP)=ai+bj+ck`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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

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

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

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

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

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

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

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

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Consider a point P in 3D coordinate system as shown in figure. What describes the point P?
1
2
3
4
The answer is "all the above". It is understood as ;; in 3D coordinates it is a, b, c. ;; as a vector representation a i + b j + c k ;; as the vector O P.
What does the word 'position' mean?
place;location
place; location
positive;desirable
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 vector O P = a i + b j + c k.
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 O P = a i + b j + c k.
What is the position vector of point 2, minus 3 by 4 ?
1
2
3
4
The answer is "2 i minus 3 by 4 j"
Given the vector O P = 3 i minus 1 point 4 j + 2 point 5 k, if O is the origin, what is the coordinate position of point p?
1
2
3
4
The answer is "3, minus 1 point 4, 2 point 5"
What is the position vector of point 0, minus 2 point 1, 3 point 4?
1
2
3
4
The answer is "minus 2 point 1 j + 3 point 4 k"

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