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[(X1-X2)2 + (Y1-Y2)2 + (Z1-Z2)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?