(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

Distance formula between two points on a 3D plane:

Sqrt[(X_{1}-X_{2})^{2}+ (Y_{1}-Y_{2})^{2}+ (Z_{1}-Z_{2})^{2}]

3. 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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# Homework Help: Perpendicular 3D Vector Problem

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