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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
mathsProperties of Vector ArithmeticsProperties of Dot Product

Dot product of a scalar multiple

In this page, you will learn about the vector dot product with the scalar multiple of a vector.



click on the content to continue..

Given `vec p = 2i+j-k` and `lambda = 3.1` what is the scalar multiple `3.1 vec p`?

  • `6.2i+3.1j-3.1k`
  • `6.2i+3.1j-3.1k`
  • `6.2i+j-k`

The answer is '`6.2i+3.1j-3.1k`'

Given the definition of dot product as
`vec p cdot vec q = |vec p||vec q|cos theta`
Dot product of a scalar multiple What is `vec p cdot (lambda vec q)`?

  • `lambda(vec p cdot vec q)`
  • `|p||lambda q|cos(theta)` if `lambda` is positive
  • `lambda|p||q|cos(theta)`
  • all the above
  • all the above

The answer is 'All the above'

Note that if `lambda` is a negative number, it equals `|p||lambda q|cos(180+theta)`.

Given the definition of dot product as
`vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z`
What is `vec p cdot (lambda vec q)`?

  • `lambda (vec p cdot vec q)`
  • `p_x(lambda q_x)+p_y(lambda q_y)+p_z(lambda q_z)`
  • `lambda (p_xq_x+p_yq_y+p_zq_z)`
  • all the above
  • all the above

The answer is 'All the above'

 •  Dot product with a scalar multiple of a vector equals the scalar multiple of the dot product with the vector.

Dot Product of scalar multiple: For any vectors `vec p, vec q`
`vec p cdot (lambda vec q) = lambda (vec p cdot vec q)`

Solved Exercise Problem:

Given that `vec p cdot vec q = 3j+1.1k`, what is `vec p/(2.1) cdot vec q`?

  • `3/(2.1)j+1.1/(2.1)k`
  • `3/(2.1)j+1.1/(2.1)k`
  • `6.3j+2.31k`
  • `3/(2.1)j+1.1k`

The answer is '`3/(2.1)j+1.1/(2.1)k`'.

                            
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