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Thought-Process to Discover Knowledge

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summary of this topic

Vector Dot Product

Vector Dot Product

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Dot Product with Added Direction


 »  By definition, dot product is scalar


 »  Some applications may specify an additional direction in the multiplication of components in parallel. In such cases, the direction is combined.

Dot product with Added Direction

plain and simple summary

nub

plain and simple summary

nub

dummy

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

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, learn about adding direction to the scalar product with an example.


Keep tapping on the content to continue learning.
Starting on learning "Dot product with added direction". ;; In this page, learn about adding direction to the scalar product with an example.

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

  • 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.vector dot product shadow example what is the length of the shadow?

  • `vec p cdot hat s`
  • length is a scalar `|p| cos theta`
  • 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`.vector dot product shadow example Is the shadow as a vector?

  • `(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`'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

your progress details

Progress

About you

Progress

An object by position vector p casts a shadow on a screen. The screen in given by unit vector s. Is the shadow a vector or scalar?
vector
a vector
scalar
a scalar
The answer is 'a vector'. The shadow is a vector that spans as a ray with a starting and end point.
vector p and screen unit vector s are given. what is the length of the shadow?
1
2
3
The answer is 'Both the above'.
An object by position vector p casts a shadow on a screen. The screen in given by unit vector s. We saw that the shadow is a vector and the length of the shadow is vector p dot hat s. Is the shadow as a vector?
1
2
3
The answer is "vector p dot 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 p and a direction given by unit vector s, the projection vector of vector p in the direction s is ; vector p dot vector s multiplied by vector s.

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