Question

Find b and c so that (5,b,c) is orthogonal to both (1,2,3) and (1,-2,1)

Answer 1

let \(v=(5,b,c)\) and \(w_1=(1,2,3)\) and \(w_2=(1,-2,1)\) solve the homogeneus linear system
\[ \large \begin{cases}
v\cdot w_1=0\\ v\cdot w_2=0
\end{cases} \]

Answer 2

I did that and I didn't get the right answer.

Answer 3

your system would be
\[ \large \begin{cases}
5+2b+3c=0\\ 5-2b+c=0
\end{cases} \]

Answer 4

adding both equations u get
\[ \large 10+4c=0\Rightarrow c=-10/4=-5/2 \]

Answer 5

then
\[ \large 5-2b+(-5/2)=0\Rightarrow b=(5/2-5)/(-2)=5/2-5/4=5/4 \]

Answer 6

Thank you!

Answer 7

u r welcome