# Homework Help: Perpendicular 3D Vector Problem

1. Feb 5, 2010

### dayyou

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?

2. Feb 5, 2010

### ehild

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

ehild

3. Feb 5, 2010

### 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.

4. Feb 5, 2010