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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.

User Guide

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
think,
figure-out, &
learn.

Just keep tapping (or clicking) on the content to continue in the trail and learn.

User Guide

To make best use of nubtrek, understand what is available.

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

jogger provides the complete mathematical definition of the concepts.

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 Vector Multiplication by Scalar

Voice

Voice

Home

»  unit vector along the direction of vector is the vector divided by the magnitude
→  hat p = (vec p)/(|vec p|)

### Unit Vector along a vector

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Unit vector in the direction of a vector is the vector divided by its magnitude.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, learn how to compute unit vector along a vector.

Keep tapping on the content to continue learning.
Starting on learning "Unit Vector along a vector". ;; In this page, learn how to compute unit vector along a vector.

Given the magnitude of a vector |vec p| = 20 what is the magnitude of (vec p)/5?

• 20
• 5
• 4
• 1/4

The answer is '4'. It is (|vec p|)/(|5|).

Given the magnitude of a vector |vec p| what is the magnitude of (vec p)/(|vec p|)?

• 1
• |vec p|
• -1
• -|vec p|

Given two vectors vec p and vec q, how can you verify if the vectors are in same direction?

• directional cosines should be equal
• components along axes should be equal

The answer is 'Directional Cosines should be equal' along the respective axes.

Given two vectors vec p and (vec p)/2, are these in the same direction?

• Different directions
• Opposite directions
• Same direction

The answer is 'Same Direction'. Direction cosine of (vec p)/2 is same as that ofvec p. Please verify this by working out.

It is shown that
•  magnitude of (vec p)/(|vec p|) is 1
•  direction of (vec p)/(|vec p|) is same as that of vec p

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Unit Vector along a Vector: The unit vector along a given vector vec p is given by
hat p = (vec p)/(|p|)

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Find the unit vector along the direction of vector vec p = 2i+2j+2k

• 1/sqrt(3) (i+j+k)
• i+j+k
• 2/sqrt(3) (i+j+k)

The answer is '1/sqrt(3) (i+j+k)'.

Progress

Progress

Given the magnitude of a vector p = 20; what is the magnitude of vector p divided by 5 ?
20;twenty
20
5;five
5
4;four
4
1;one;by
1/4
Given the magnitude of a vector p, what is the magnitude of vector p divided by magnitude of vector p?
1;one
1
magnitude
magnitude of vector p
minus one;-1
minus 1
minus
minus magnitude of vector p
Given two vectors p and q, how can you verify if the vectors are in the same direction?
directional;cosines
directional cosines should be equal
components;along;axes
components along axes should be equal
The answer is 'Directional Cosines should be equal' along the respective axes.
Given two vectors p and p divided by 2, are these in the same direction?
different
Different directions
opposite
Opposite directions
same
Same direction