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Thought-Process to Discover Knowledge

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User Guide

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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.

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User Guide

trek is the step by step exploration of the concept.

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User Guide

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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

### Vector Cross Product

Voice

Voice

Home

Vector Cross Product : First Principles

»  multiplied with component in perpendicular
→  vec p xx vec q   =vec p xx vec b = |vec p||vec b| hat n

→  product of magnitudes of components in perpendicular

→  direction perpendicular to both the vectors

### Cross Product: First Principles

plain and simple summary

nub

plain and simple summary

nub

dummy

Vector Cross Product is defined as the product of components in perpendicular.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, the vector cross product is explained in first principles.

Keep tapping on the content to continue learning.
Starting on learning "First Principles of Vector Cross Product". ;; In this page, the vector cross product is explained in first principles.

The product where vector components in perpendicular interact is defined. Given vectors vec p and vec q as shown in figure. What is the component of vec q perpendicular to the vec p?

• vec a
• vec b
• ai+bj
• bj+ai

The answer is 'vec b'

Given vec q with component vec b in perpendicular to vec p as shown in figure. The angle between the vectors is theta. What is |vec b|?

• |q|sin theta
• |q|cos theta
• |p|sin theta
• |p|cos theta

The answer is '|q|sin theta'

Given vectors vec p and vec q and the product between them as shown in the figure. What will be a good choice of direction of the product between components in perpendicular?

Two intersecting lines, which are not parallel, define a plane. The normal on the face of the plane describes the plane and so, the normal is taken as the direction of the product.

A plane can be described by

•  normal which is one side of the plane, or

•  the negative of the normal, which is the other side of the plane. Which one is chosen for the vector cross product vec p xx vec q?

The direction of the cross product vec p xx vec q. In a standard right-handed rectangular coordinate system,
The direction in which a standard screw advances when it turns from vec p to vec q, defines the normal.

The direction of the cross product vec p xx vec q. In a standard right-handed rectangular coordinate system,
The direction pointed by the right thumb when fingers are curled to point from vec p to vec q, defines the normal.

Formal definition of vector cross product.
vec p xx vec q = |p||q|sin theta hat n where hat n is the normal denoting the direction of right handed rotation from vec p to vec q.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Vector Cross Product: for vectors vec p, vec q in bbb(R)^3
vec p xx vec q = (|p||q|sin theta ) hat n
where hat n is the unit vector of right-handed rotation from vec p to vec q.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Progress

Progress

The product where vector components in perpendicular interact is defined. Given vectors vector p and vector q as shown in figure. What is the component of vector q perpendicular to the vector p?
1
2
3
4
Given vector q with component vector b in perpendicular to vector p as shown in figure. The angle between the vectors is theta. What is magnitude of vector b?
1
2
3
4
The answer is "magnitude of q multiplied sine theta"
Given vectors vector p and vector q and the product between them as shown in the figure. What will be a good choice of direction of the product between components in perpendicular?;; Two intersecting lines, which are not parallel, define a plane. The normal on the face of the plane describes the plane and so, the normal is taken as the direction of the product.
A plane can be described by ;; normal which is one side of the plane or the negative of the normal which is the other side of the plane. Which one is chosen for the vector cross product vector p cross vector q?
The direction of the cross product vector p cross vector q. In the standard right-handed rectangular coordinate system, the direction in which a standard screw advances when it turns from vector p to vector q, defines the normal.
The direction of the cross product vector p cross vector q. In the standard right-handed rectangular coordinate system, the direction pointed by the right thumb when fingers are curled to point from vector p to vector q defines the normal.
Formal definition of vector cross product: vector p cross vector q = magnitude of p multiplied magnitude q sine theta multiplied n hat. Where n hat is the normal denoting the direction of right handed rotation from vector p to vector q.
Vector Cross Product is defined as the product of components in perpendicular.
Vector Cross Product: for vectors p , q in real-numbers 3 dimensional space, vector p cross vector q = magnitude of p, magnitude of q, sine theta, multiplied n hat. where n hat is the unit vector of right-handed rotation from vector p to vector q.

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