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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.

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mathsVector AlgebraProperties of Cross Product

### Cross Product of Collinear Vectors

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When two vectors are called 'collinear' vectors? color(coral)(text(co)) + color(deepskyblue)(text(linear)) means color(coral)(text(together))+color(deepskyblue)(text(on a line))

• the angle between vectors 0^@
• the angle between vectors 180^@
• the vectors are parallel
• all the above
• all the above

The answer is 'All the above'

Given the definition of cross product as
vec p xx vec q = |vec p||vec q|sin theta hat n
What is vec p xx vec q, if the given vectors are collinear?

• |p||q|sin 0 hat n
• |p||q|sin 180 hat n
• 0
• 0
• all the above

The answer is 'all the above'. The angle between Collinear vectors can be either 0^@ or 180^@. And sin0 = sin180 = 0.

Given two non-zero vectors vec p, vec q in bbb V have vec p xx vec q = 0, then what is the angle between the vectors?

• 0^@
• 0^@
• 90^@
• 270^@
• Any one of the above

The answer is '0^@'. It can either be 0^@ or 180^@.

•  Cross product of parallel vectors is 0 or null vector.

Cross Product of Collinear Vectors: For any pair of collinear vectors vec p, vec q in bbb V,
vec p xx vec q =0

Angle between vectors when cross product is 0: For any pair of non-zero vectors vec p, vec q in bbb V, If vec p xx vec q = 0 then the vectors are collinear. The angle between them is 0^@ or 180^@.

Solved Exercise Problem:

Given vec p= 2i+3.1j+.5k and vec q = 2i+3.1j+.5k what is the angle between them?

• 90^@
• 45^@
• 180^@
• 0^@
• 0^@

The answer is '0^@'. The vectors are identical.

Solved Exercise Problem:

Given a vector vec p with magnitude 12, what is vec p xx vec p?

• 12
• sqrt(12)
• 12xx12
• 0
• 0

The answer is '0'.

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