# Thread: find a vector perpendicular to both vector a and vector b

1. ## find a vector perpendicular to both vector a and vector b

I did this one the way I did a previous problem like this but came up with a completely incorrect answer

the question is:
vector a = (2,1,0) and vector b = (-1,6,1) find a vector perpendicular to both.

2. $\displaystyle ||a\times b||=\begin{vmatrix}i&j&k\\2&1&0\\-1&6&1\end{vmatrix}=\mbox{normal vector}$

3. how about using dot product? haven't got to cross product yet

4. The dot product produces a scalar not a vector.

how about using dot product? haven't got to cross product yet
Have you ever taking a determinant of a matrix?

6. You could use the dot product by setting up a system of two equations in three unknowns. That is, your unknown vector is r=(x,y,z). Set the dot product of r with both your initial vectors equal to zero, and solve the resulting system.

7. no, haven't gotten to that point

8. Originally Posted by Ackbeet
You could use the dot product by setting up a system of two equations in three unknowns. That is, your unknown vector is r=(x,y,z). Set the dot product of r with both your initial vectors equal to zero, and solve the resulting system.
yeah, I tried that, thats how I've done it before, didn't work out. perhaps its time for a math break.