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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.

Read in the blogs more about the unique learning experience at nubtrek.
mathsVector AlgebraVector Dot Product

### Vector Dot Product : Projection of a vector

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Vector dot product is understood as product between components in parallel to each other.
In finding the component in parallel to one vector the vector is projected on to another in the figure, What is a ?

• a is the projection of vec q onto vec p
• a is the projection of vec q onto vec p
• a is the projection of vec p onto vec q

The answer is 'a is the projection of vec q onto vec p'

The vector dot product can be used to find projection of a vector on a line.

Consider the line given by vec s and the vector vec p as shown in the figure. We know that vec s cdot vec p = |vec s| |vec p| cos theta.
To find the projection of vec p on vec s, which of the following can be used?

• hat s cdot vec p, where hat s is unit vector
• (vec s)/(|vec s|) cdot vec p
• both the above
• both the above

The answer is 'both the above'.

Vector dot product can be used to find projection of a vector on a line or on another vector.

Projection of a vector: Projection of a vector vec p on a line in direction vec s is
= vec p cdot hat s
where hat s is the unit vector along vec s.

Solved Exercise Problem:

Two vectors vec p and vec q with magnitudes 2 and 3 respectively are at an angle 60^@. What is the projection of vec p on vec q?

• 2 xx cos 60^@
• 2 xx 1/2
• 1
• all the above
• all the above

The answer is 'All the above'.

slide-show version coming soon