Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

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 Cross Product

Voice

Voice

Home

»  vector cross product is bilinear
→  vec p xx (lambda vec q + vec r)   = lambda (vec p xx vec q)   + vec p xx vec r

### Bilinear Property

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Cross product is bilinear.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

Support Nubtrek

You are learning the free content, however do shake hands with a coffee to show appreciation.
To stop this message from appearing, please choose an option and make a payment.

Keep tapping on the content to continue learning.
Starting on learning "Bilinear Property". ;; In this page, you will learn about the bilinear property of vector cross product.

Cross product is defined between vec p, vec q in bbb V and the result vec p xx vec q in bbb V. This can be considered as a transformation. What type of transformation is this?

• unary
• binary
• ternary

The answer is 'binary' as the input is two vectors. 'bi' means two.

Which of the following property is true for Bilinear transformation?

• T(x+y, z)=T(x,z)+T(y,z)
• T(ax,z)=aT(x,z)
• T(ax+y, z)= aT(x,z)+T(y,z)
• All the above

The answer is 'All the above'.

The property T(ax+y, z)= aT(x,z)+T(y,z) defines linearity for binary operator T. That is why it is named Bi-linear.

Consider the cross product as a binary transform T(vec p, vec q) = vec p xx vec q. Is cross product bilinear?

• Yes
• No

The answer is 'Yes'. The cross product is distributive over vector addition and also satisfies the scalar multiple property.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Bilinear Property: For any vector vec p, vec q, vec r in bbb V and lambda in RR
(lambda vec p + vec q) xx vec r = lambda (vec p xx vec r) + (vec q xx vec r)

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given vec x xx vec z = 2 and vec y xx vec z = 1, what is (3 vec x + 2 vec y) xx vec z?

• 5
• 6
• 8
• 9

The answer is '8'
(3 vec x + 2 vec y) xx vec z
quad = 3 vec x xx vec z + 2 vec y xx vec z

Progress

Progress

Cross product is defined between vector p, vector q in vector space v, and the result vector p cross vector q in vector space v. This can be considered as a transformation. What type of transformation is this?
unary
unary
binary
binary
ternary
ternary
The answer is 'binary' as the input is two vectors. 'bi' means two.
Which of the following property is true for Bilinear transformation?
1
2
3
4
The answer is "All the above". The property T of a x + y, z, = , a T of x, z, +, T of y, z. defines linearity for binary operator T. That is why it is named bi-linear.
Consider the cross product as a binary transform: T of vector p, vector q , =, vector p, cross, vector q. Is cross product bilinear?
yes;s
Yes
no
No
The answer is 'Yes'. The cross product is distributive over vector addition and also satisfies the scalar multiple property.
Cross product is bilinear.
Bilinear Property: For any vector p, q, r in vector space v and lambda in real numbers;; lambda times vector p + vector q, cross vector r = lambda times vector p cross vector r, +, vector q cross vector r.
Given vecor x cross vector z = 2 and vector y cross vector z = 1, whatis 3 vector x + 2 vector y cross vector z?
5
5
6
6
8
8
9
9