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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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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.

click on the content to continue..

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

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'.

slide-show version coming soon