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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 AlgebraProperties of Vector Multiplication by Scalar

Multiplication by Product of Scalars

In this page, multiplication of a vector by product of scalars is explained.



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Given that `vec p = ai+bj+ck` and `lambda, mu` where `a,b,c,lambda,mu in bbb R`, What will be the result of `(lambda mu) vec p `?multiplication by two scalars

  • `lambda(mu vec p)`
  • `lambda(mu vec p)`
  • `lambda vec p mu vec p`
  • `mu vec p

The answer is '`lambda(mu vec p)`'. This is proven by multiplying the components individually by the scalar.

 •  Multiplication of vector by a product of two scalars is equivalently multiplication by the scalars one by one.

Multiplication by Product of scalars: Given a scalar as product of two scalars `lambda mu`,
`(lambda mu)vec p = lambda(mu vec p)`

                            
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