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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 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
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'.

slide-show version coming soon