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Thought-Process to Discover Knowledge

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  nub,

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User Guide    

nub is the simple explanation of the concept.

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summary of this topic

Vector Addition

Vector Addition

Voice  

Voice  



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Vector Addition : Component form


 »  individual components add
    →  `r_x = p_x+q_x`
    →  `r_y = p_y+q_y`
    →  `r_z = p_z+q_z`

Vector Addition in Component form

plain and simple summary

nub

plain and simple summary

nub

dummy

When vectors in the component form are added, the corresponding components are added.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, learn how two vectors in component form add up.


Keep tapping on the content to continue learning.
Starting on learning "Component form of vector addition". ;; In this page, you will learn how two vectors in component form add up.

What is the component form of a vector?

  • components along `x, y,` and `z` axes
  • magnitude of the vector
  • directional cosines of vector

Answer is 'components along `x, y,` and `z` axes'

In the component form, two vectors are considered `a i` and `p i`. What is the result of addition of two vectors `a i` and `p i` ?

  • `(a+p)i`
  • cannot be added.

Answer is '`(a+p)i`'.
The magnitudes add up as two vectors are in the same direction `i` , that is, along x-axis.

What is the result of addition of two vectors `ai+bj` and `p i` ?

  • `(a+p)i+bj`
  • cannot be added, as the vectors are in different directions.

Answer is '`(a+p)i+bj`'. The magnitudes add up along the directions in parallel and the directions in perpendicular are kept separately. In this problem, in the direction of x-axis, `a i` and `p i` are given. They are added in magnitude.

What is the result of addition of two vectors `a i+b j+c j` and `p i+q j+r k` ?

  • `(a+p)i+(b+q)j+(c+r)k`
  • cannot be added, as the vectors are in different directions.

Answer is '`(a+p)i+(b+q)j+(c+r)k`'. The magnitudes add up along the directions in parallel and the directions in perpendicular are kept separately. In these two vectors, the components along the three axes are given in component form.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Addition of two vectors: When two vectors `vec p = p_x i+p_yj+p_zk` and `vec q = q_x i+q_yj+q_zk` are added the result is `vec p + vec q = (p_x+q_x)i + (p_y+q_y)j + (p_z+ q_z)k`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

your progress details

Progress

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Progress

What is the component form of a vector?
components;along;x;y;z;axes
components along x, y, and z axes
magnitude
magnitude of the vector
directional;cosines
directional cosines of vector
Answer is 'components along x, y, and z axes'
In the component form, two vectors are considered a i and p i . What is the result of addition of two vectors a i and p i ?
1
2
Answer is '(a+p) i'. ;; The magnitudes add up as two vectors are in the same direction i , that is, along x-axis.
What is the result of addition of two vectors ai+bj and p i ?
1
2
Answer is ' (a+p)i+bj '. The magnitudes add up along the directions in parallel and the directions in perpendicular are kept separately. In this problem, in the direction of x-axis, a i and p i are given. They are added in magnitude.
What is the result of addition of two vectors a i+b j+c j and p i+q j+r k ?
1
2
Answer is ' (a+p)i+(b+q)j+(c+r)k '. The magnitudes add up along the directions in parallel and the directions in perpendicular are kept separately. In these two vectors, the components along the three axes are given in component form.
When vectors in the component form are added, the corresponding components are added.
Addition of two vectors: When two vectors p = p x i+p y j+p z k and vector q = q x i+q y j+q z k are added the result is vector p + vector q = (p x+q x)i + (p y+q y)j + (p z+ q z)k

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