Perpendicular 3D Vector Problem

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Homework Help Overview

The discussion revolves around finding a vector that is perpendicular to the vector [6,2,3] while maintaining the same length. The original poster expresses uncertainty about how to determine the length of the vector and the concept of perpendicularity in three-dimensional space.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to relate the problem to 2D space and considers the implications of finding a perpendicular vector in 3D. They express confusion about the length of the vector due to the lack of a second point. Questions about the scalar product and its relevance to determining perpendicularity are also raised.

Discussion Status

Participants are exploring the concepts of vector perpendicularity and length. Some guidance has been offered regarding the scalar product, but there is no explicit consensus on the approach to take. The original poster is seeking further clarification on the concepts discussed.

Contextual Notes

The original poster mentions being a sophomore in high school and indicates that they have not yet learned about the scalar or dot product, which may limit their understanding of the problem.

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Homework Statement


Give an example of a vector perpendicular to [6,2,3] that has the same length.

Homework Equations


Distance formula between two points on a 3D plane:
Sqrt[(X1-X2)2 + (Y1-Y2)2 + (Z1-Z2)2]

The Attempt at a Solution


In 2D space, the perpendicular vector of [X,Y] is [-Y,X]. However, I know that 3D vectors have an infinite number of perpendicular vectors. Then I thought to myself that I should use the distance between to points to figure out the length, but since the problem does not give me the second point, I do not know what the length of the line is. I was thinking of starting at the origin, since the line from the origin to the point is the hypotenuse of the triangle the points make in 3D. I got 6.2, but now do not know how to go from here. Help is very appreciated.

P.S. Just for further learning, how would I show that two vectors are perpendicular in the same equation?
 
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Have you learned about "scalar product" or "dot product" of two vectors?

ehild
 
No, not yet. Only a sophmore in high school. If those concepts A) are on the SAT and B) help me find the answer, an explanation would be very appreciated.
 

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