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dayyou
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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?