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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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Vector Dot Product: Projection form


 »  component in parallel is calculated by the angle
    →  `vec p cdot vec q` ` = |vec p| |vec q| cos theta`
    →  Note that `|vec a| = |vec q|cos theta`
    →  `vec a` is the projection of `vec q` on `vec p`

Vector Dot Product : Projection of a vector

plain and simple summary

nub

plain and simple summary

nub

dummy

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

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, you will learn about computing projection of vector using vector dot product.


Keep tapping on the content to continue learning.
Starting on learning "vector dot product in the form, projection of a vector". ;; In this page, you will learn about computing projection of vector using vector dot product.

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 anothervector dot product projection form in the figure, What is `a` ?

  • `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. vector dot product projection form

Consider the line given by `vec s` and the vector `vec p` as shown in the figure.vector dot product projection form 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

The answer is 'both the above'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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

The answer is 'All the above'.

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Progress

About you

Progress

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?
1
2
The answer is "a is the projection of vector q onto vector p"
The vector dot product can be used to find projection of a vector on a line.
Consider the line given by vector s and the vector p as shown in the figure. We know that vector s dot vector p = magnitude of vector s multiplied magnitude of vector p multiplied cos theta. ; To find the projection of vector p on vector s, which of the following can be used?
1
2
3
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 p on a line in direction vector s is ; vector p dot hat s ; where hat s is the unit vector along vector s.
Two vector p and q with magnitudes 2 and 3 respectively are at an angle 60 degree. What is the projection of vector p on vector q?
1
2
3
4
The answer is "all the above".

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