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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.
mathsProperties of Vector ArithmeticsProperties of Vector Multiplication by Scalar

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Considering that a vector has components as real numbers, Given that vec p = ai+bj+ck, vec q = e i + fj + g k and lambda  where a,b,c,d,e,f,lambda in bbb R, What will be the result of lambda (vec p + vec q)?

• scalar
• lambda vec p + lambda vec q
• lambda vec p + lambda vec q
• lambda vec p + vec q

The answer is 'lambda vec p + lambda vec q'. This is proven by multiplying the components individually by the scalar and using vector addition properties.

•  A scalar multiplied by sum of two vectors equals sum of vectors multiplied by the scalar.

Distributive over Vector Addition: Given scalar lambda and vectors vec p, vec q,
lambda(vec p + vec q) = lambda vec p + lambda vec q

Solved Exercise Problem:

Given that vec p = 6 vec q and vec r = 4 vec s, which of the following equals 3 ( 2vec q+ 4/3 vec s)?

• vec p + vec r
• vec p + vec r
• vec p + 2 vec r
• vec p - vec r
• vec r - vec p

The answer is 'vec p + vec r'.

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