Perpendicular 3D Vector Problem

[dayyou]

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?

 

[ehild]

Have you learned about "scalar product" or "dot product" of two vectors?

ehild

 

[dayyou]

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.

 

[ehild]

Go to here and read from "Representation of a vector".

http://en.wikipedia.org/wiki/Euclidean_vector. Then come back. ehild