Perpendicular 3D Vector Problem

AI Thread Summary
To find a vector perpendicular to [6,2,3] with the same length, one can utilize the concept that 3D vectors have infinite perpendiculars. The length of the vector can be calculated using the distance formula, but without a second point, determining the exact length is challenging. Starting from the origin can help visualize the problem, as the vector from the origin to [6,2,3] forms a triangle in 3D space. The discussion also touches on the scalar or dot product as a method to demonstrate perpendicularity between vectors. Understanding these concepts is essential for solving the problem effectively.
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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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