find a vector that has this characteristic

**superdude** · February 8th 2010, 03:38 PM

find a vector u=(a,b,c) where a,b,c are not all 0 so that u is orthogonal to both x=(1,2,1) and y=(1,-1,1)

Can I use the cross product on x and y or would that be incorrect?

**tonio** · February 8th 2010, 06:41 PM

Originally Posted by superdude

find a vector u=(a,b,c) where a,b,c are not all 0 so that u is orthogonal to both x=(1,2,1) and y=(1,-1,1)

Can I use the cross product on x and y or would that be incorrect?

Of course you can cross multiply the vectors and that's correct: the cross product is a vector orthogonal to both original ones.

Tonio

**math2009** · February 9th 2010, 04:17 AM

There is another method except cross product.

$ A=\begin{bmatrix} \vec{x} &\vec{y} \end{bmatrix}~, ~\vec{u}\in im(A)^{\perp}=\ker(A^{T}) =\ker\begin{bmatrix} 1 &2 &1 \\ 1 &-1 &1 \\ \end{bmatrix} \\ $

$ =\ker\begin{bmatrix} 1 &2 &1 \\ 0 &-3 &0 \\ \end{bmatrix} =\ker\begin{bmatrix} 1 &0 &1 \\ 0 &1 &0 \\ \end{bmatrix} =span( \begin{bmatrix} -1 \\0 \\1 \end{bmatrix} ) \\ $

$ \rightarrow b=0,|a|=|c|\neq 0,a=-c $

If dimension is high, cross product is complex

Thread: find a vector that has this characteristic

LinkBack

Thread Tools

Display

find a vector that has this characteristic

Similar Math Help Forum Discussions

How to find the determinant of matrix if given characteristic equation only?

Find characteristic root.

Find the characteristic roots and characteristic vector

find the diagonalization of this matrix and its characteristic poly.

Characteristic Value and Vector

Search Tags