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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