Vector Cross Product Homework: Solving AxB with B values of 8i+16j and -8i-16j

AI Thread Summary
The cross product of vectors A = 2i + 4j and B = 8i + 16j results in zero, as both vectors are parallel, indicating they are scalar multiples of the same unit vector. Similarly, the cross product of A and B = -8i - 16j also yields zero for the same reason. The discussion emphasizes that the relationship between A and B allows for this conclusion without detailed computation. The key takeaway is that parallel vectors produce a cross product of zero. Understanding vector directionality is crucial in determining the outcome of the cross product.
noeinstein
Messages
14
Reaction score
0

Homework Statement



Given that A = 2i + 4j, evaluate each of the following. (Hint: This question can be answered without computation.)

(a) What is AxB when B = 8i + 16j?

(b) What is AxB when B = -8i - 16j?

Homework Equations



AxB=(Axi + Ayj) x (Bxi +Byj)
=(AxBx)(i x i) + (AxBy)(i x j) + (AyBx)(j x i) + (AyBy)(j x j)
AxB=(AxBy - AyBx)k

The Attempt at a Solution



AxB= (2 x 16)k - (4 x 8)k= 0k
 
Physics news on Phys.org
Indeed.

Can you see the relation between A and B that makes the zero result trivial, i.e you can solve it "without" computation?
 
They have the same/opposite direction?
 
Geeze no kidding! dahh. Thanks
 
noeinstein said:
They have the same/opposite direction?

Indeed.
The vectors involved are parallell. Therefore, their cross product must be 0.
 
Try parallel or colinear. They are scalar multiples of the same unit vector.
 
Thread 'Voltmeter readings for this circuit with switches'

Thread 'Voltmeter readings for this circuit with switches'

TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
View full post »
Thread 'Correct statement about a reservoir with an outlet pipe'

Thread 'Correct statement about a reservoir with an outlet pipe'

The answer to this question is statements (ii) and (iv) are correct. (i) This is FALSE because the speed of water in the tap is greater than speed at the water surface (ii) I don't even understand this statement. What does the "seal" part have to do with water flowing out? Won't the water still flow out through the tap until the tank is empty whether the reservoir is sealed or not? (iii) In my opinion, this statement would be correct. Increasing the gravitational potential energy of the...
View full post »

Similar threads

Calculate Torque on a Particle with Given Force and Position | Homework Solution
Replies
6
Views
5K
Calculating Vectors and Components: Finding A*B and AxB Components
Replies
6
Views
2K
Help with unit vector for a magnetic field
Replies
5
Views
2K
Physics Vector Cross Product problem
Replies
6
Views
3K
Physics 221 Calc-based question for homework
Replies
23
Views
3K
Finding dot product, cross, and angle between 2 vectors
Replies
3
Views
1K
Finding the Angle Between Vectors A and B in the Cross Product
Replies
13
Views
2K
Need Help Finding the Angle Between Two Vectors
Replies
2
Views
13K
Finding Components of Cross Product for Vectors A and B
Replies
5
Views
3K
Vector Cross Product Homework: Find 3rd Vector Perpendicular to C & D
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top