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Thought-Process to Discover Knowledge

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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.

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trek,

jogger,

exercise.

User Guide

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User Guide

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User Guide

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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 a scalar multiple
→  vec p xx (lambda vec q) = lambda (vec p xx vec q)

### Cross product of a Scalar Multiple

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Cross product with a scalar multiple of a vector equals scalar multiple of the cross 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 cross product with scalar multiple of a vector.

Keep tapping on the content to continue learning.
Starting on learning "Cross product of a Scalar Multiple". ;; In this page, you will learn about the vector cross product with 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 cross product as
vec p xx vec q = |vec p||vec q|sin theta hat n
What is vec p xx (lambda vec q)?

• lambda(vec p xx vec q)
• |p||lambda q|sin(theta) hat n if lambda is positive
• lambda|p||q|sin(theta) hat n
• all the above

The answer is 'All the above'

Note that if lambda is a negative number, it equals |p||lambda q|sin(180+theta) hat n.

Given the definition of cross product as
vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|
What is vec p xx (lambda vec q)?

• lambda (vec p xx vec q)
• |(i, j, k),(p_x, p_y, p_z),(lambda q_x, lambda q_y, lambda q_z)|
• lambda |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|
• all the above

The answer is 'All the above'

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given that vec p xx vec q = 3j+1.1k, what is vec p/(2.1) xx 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 vector p?
1
2
The answer is "6 point 2 i + 3 point 1 j minus 3 point 1 k"
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, lambda 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 times q, sine 180 + theta, n hat.
Given the definition of cross product as vector p cross vector q in determinant form, what is vector p, cross, lambda, times, vector q?
1
2
3
4
The answer is 'All the above'
Cross product with a scalar multiple of a vector equals scalar multiple of the cross product with the vector.
Cross Product of scalar multiple: For any vectors p and q; vector p, cross, lambda vector q, =, lambda, vector p,cross,vector q.
Given that vector p cross vector q = 3j + 1 point 1 k, what is vector p by 2 point 1, cross vector q?
1
2
3
The answer is "3 divided by 2 point 1 j + 1 point 1 divided by 2 point 1 k"

we are not perfect yet...