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
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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
 
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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.
 

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