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 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanged mass'

Thread 'A cylinder connected to a hanged mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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