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Thought-Process to Discover Knowledge

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User Guide

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think,
figure-out, &
learn.

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User Guide

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nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about.

User Guide

trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step.

User Guide

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This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen.

User Guide

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge.

summary of this topic

### Properties of Cross Product

Voice

Voice

Home

»  cross product of collinear vectors

→  theta = 0^@

→  sin 0^@ = 0

→  vec p xx vec q = vec 0

### Cross Product of Collinear Vectors

plain and simple summary

nub

plain and simple summary

nub

dummy

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

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Starting on learning "cross product between two collinear vectors".

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

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

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

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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^@.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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

• 90^@
• 45^@
• 180^@
• 0^@

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

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

• 12
• sqrt(12)
• 12xx12
• 0

The answer is '0'.

Progress

Progress

When two vectors are called 'collinear' vectors?
1
2
3
4
The answer is 'All the above'
Given the definition of cross product as vector p cross vector q = magnitude of p, magnitude of q, sine theta n hat; what is vector p cross vector q, if the given vectors are collinear?
1
2
3
4
The answer is "either one of the above". The angle between collinear vectors can be either 0 degree or 180 degree. And sine 0 = sine 180 = 0.
Given two non-zero vectors vector p, vector q in vector space v, have vector p cross vector q = 0, then what is the angle between the vectors?
1
2
3
4
The answer is "0 degree ". It can either be 0 degree or 180 degree.
Cross product of collinear vectors is 0 or null vector.
Cross Product of Collinear Vectors: For any pair of collinear vectors p, q in vector space v;; vector p cross vector q = 0.
Angle between vectors when cross product is 0 : For any pair of non-zero vectors p, q in vector space v, if vector p cross vector q = 0, then the vectors are collinear. The angle between them is 0 degree or 180 degree.
Given vectors p and q, what is the angle between them?
1
2
3
4
The answer is "0 degree". The vectors are identical.
Given vector p with magnitude 12, what is vector p cross vector p?
1
2
3
4
The answer is ' 0 '.

we are not perfect yet...