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summary of this topic

Properties of Cross Product

Properties of Cross Product

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 »  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

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In this page, you will learn about the bilinear property of vector cross product.


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`

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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
The answer is "8".

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