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Thought-Process to Discover Knowledge

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mathsVector AlgebraProperties of Vector Multiplication by Scalar

Magnitude of a scalar multiple of a vector

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`.

slide-show version coming soon