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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.

Read in the blogs more about the unique learning experience at nubtrek.continue

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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`

*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.

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`

*your progress details*

Progress

*About you*

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

The answer is "8".