Find Unit Vector Orthogonal to A in Plane B & C

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Homework Help Overview

The problem involves finding a unit vector that is orthogonal to vector A within the plane defined by vectors B and C. The vectors are given as A=2i-j+k, B=i+2j+k, and C=i+j-2k.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the cross product of vectors B and C as a potential method to find the orthogonal vector. There is consideration of the need to convert the resulting vector into a unit vector.

Discussion Status

Some participants have offered guidance on the necessity of calculating the unit vector from the cross product result. There is acknowledgment of the correctness of the cross product approach, but no consensus on the final answer has been reached.

Contextual Notes

Participants are working under the assumption that the calculations for the cross product are correct, but there is no explicit verification of the calculations provided in the discussion.

MozAngeles
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Homework Statement



Find a unit vector orthogonal to A in the plane B and C if A=2i-j+k B=i+2j+k and C=i+j-2k

Homework Equations





The Attempt at a Solution


Im thinking the solution is to take the cross product of B and C. and that would be the solution??
 
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MozAngeles said:

The Attempt at a Solution


Im thinking the solution is to take the cross product of B and C. and that would be the solution??

BxC would give satisfy the conditions yes, but you will need to get the unit vector of BxC.
 
So my answer would be 1/[tex]\sqrt{35}[/tex](5i+3k-j)?
 
Yes, assuming you calculated BxC correctly.
 

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