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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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User Guide

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
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 Dot Product

Voice

Voice

Home

»  vector dot product of scalar multiple
→  vec p cdot (lambda vec q) = lambda (vec p cdot vec q)

### Dot product of a scalar multiple

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Dot product with a scalar multiple of a vector equals the scalar multiple of the dot product with the vector.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, you will learn about the vector dot product with the scalar multiple of a vector.

Keep tapping on the content to continue learning.
Starting on learning "Dot product of a scalar multiple". ;; In this page, you will learn about the vector dot product with the scalar multiple of a vector.

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+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

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

The answer is 'All the above'

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Dot Product of scalar multiple: For any vectors vec p, vec q
vec p cdot (lambda vec q) = lambda (vec p cdot vec q)

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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
• 6.3j+2.31k
• 3/(2.1)j+1.1k

The answer is '3/(2.1)j+1.1/(2.1)k'.

Progress

Progress

Given vector p = 2i + j minus k and lambda = 3 point 1, what is the scalar multiple 3 point 1 multiplied vector p?
1
2
The answer is "6 point 2 i + 3 point 1 i minus 3 point 1 k"
Given the definition of dot product as vector p dot vector q = magnitude of vector p, magnitude of vector q, cos theta. What is vector p dot lambda times vector q?
1
2
3
4
The answer is "All the above". Note that if lambda is a negative number, it equals magnitude of p, magnitude of lambda q, cos 180 + theta.
Given the definition of dot product as vector p dot vector q = p x q x + p y q y + p z q z. What is vector p dot lambda times vector q?
1
2
3
4
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 p and q ;; vector p dot, lambda times vector q =, lambda times, vector p dot vector q.
Given that vector p dot vector q = 3j + 1 point 1 k, what is vector p divided by 2 point 1, dot vector q?
1
2
3
The answer is "3 divided by 2.1 j + 1 point 1 divided by 2 point 1 k"

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