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

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Homework Help Overview

The problem involves evaluating the vector cross product of A = 2i + 4j with two different vectors B: 8i + 16j and -8i - 16j. The context is within vector mathematics, specifically focusing on properties of cross products.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between vectors A and B that leads to a zero result for the cross product, suggesting that they may be parallel or collinear. There is an exploration of the implications of this relationship without performing explicit calculations.

Discussion Status

The discussion is exploring the conceptual understanding of why the cross product results in zero, with participants affirming the idea that the vectors are scalar multiples of one another. There is a recognition of the trivial nature of the result based on the vectors' alignment.

Contextual Notes

Participants are considering the implications of vector direction and magnitude in the context of the cross product, focusing on the geometric interpretation rather than computational methods.

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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