Question

find the cross product of the vectors (2, -1, 4) and (6, -2,1). is the resulting vector perpendicular to the given vector?

Answer 1

To find the cross product just plug the two vectors into a matrix like so: \[\begin{matrix}
i & j & k \\
2 & -1 & 4 \\
6 & -2 & 1
\end{matrix}\]
And then take the determinant, we should give you the cross product as \[\left<7, 22, 2\right>\] To check to see if it is perpendicular, just take the dot product of this vector with your two original vectors; if the dot product is zero, the vectors are perpendicular. However, it is a fact that the cross product of two vectors is ALWAYS perpendicular to the two original vectors, so they must be.