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Thought-Process to Discover Knowledge

Welcome to nubtrek.

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

### Dot product with Added Direction

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An object by position vector vec p casts a shadow on a screen. The screen in given by unit vector vec s Is the shadow a vector or scalar?

• a vector
• a vector
• a scalar

The answer is 'a vector'. The shadow is a vector that spans as a ray with a starting and end point.

vec p and the screen hat s are given. what is the length of the shadow?

• vec p cdot hat s
• length is a scalar |p| cos theta
• both the above
• both the above

The answer is 'Both the above'.

An object by position vector vec p casts a shadow on a screen. The screen in given by unit vector vec s. We saw that the shadow is a vector and the length of the shadow is vec p cdot hat s. Is the shadow as a vector?

• (vec p cdot hat s) hat s
• (vec p cdot hat s) hat s
• (vec p cdot hat s) hat p
• (vec p cdot hat s) vec p

The answer is '(vec p cdot hat s) hat s'.

Vector dot product by definition is a scalar. Depending on the application requirement, a direction can be added to the scalar.

Projection vector using Dot Product: For a vector vec p and a direction given by unit vector hat s, the projection vector of vec p in direction hat s is (vec p cdot hat s) hat s.

slide-show version coming soon