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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.

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mathsVector AlgebraVector Addition

Vector Addition in Component form

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



click on the content to continue..

What is the component form of a vector?

  • components along `x, y,` and `z` axes
  • 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`
  • `(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`
  • `(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`
  • `(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.

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

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`

                            
slide-show version coming soon