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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.continue

In this page, you will learn how to find the magnitude of a scalar multiple of a vector.



click on the content to continue..

What is the magnitude of `vec p = ai+bj+ck`?

  • `|vec p|=sqrt(a+b+c)`
  • `|vec p|=sqrt(a^2+b^2+c^2)`
  • `|vec p|=sqrt(a^2+b^2+c^2)`
  • `|vec p|=a^2+b^2+c^2`

The answer is '`|vec p|=sqrt(a^2+b^2+c^2)`'

What is the magnitude of `lambda vec p` if `vec p = ai+bj+ck`?

  • `|lambda p| = sqrt((lambda a)^2+(lambda b)^2+(lambda c)^2)`
  • `|lambda p| = sqrt(lambda^2) sqrt(a^2+b^2+c^2)`
  • `|vec p|=|lambda| |vec p|`
  • all the above
  • all the above

The answer is 'All the above'. The options are the steps to prove that `|lambda vec p|=|lambda| |vec p|`

 •  Magnitude of scalar multiple of a vector is product of magnitudes of the scalar and the vector.

Magnitude of Scalar Multiple of Vector: Given scalar `lambda` and vector `vec p`,
`|lambda vec p| = |lambda||vec p|`

Solved Exercise Problem:

Given `|vec p| = 2`, what is `|-7 vec p|`?

  • `-14`
  • `14`
  • `14`
  • `2`
  • `-7`

The answer is '`14`'. `|-7 vec p| = |-7||vec p| = 7 xx 2`.

                            
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