QUESTIONS - LINEAR ALGEBRA - VECTORS

QUESTIONS / ANSWERS .ACF.LINEAR ALGEBRA
On 2/9/07, acf wrote:
> acf has sinistral a recent animadversion on your put "QUESTIONS - LINEAR ALGEBRA &
> VECTORS":
>
> Let B and C be non-equality vectors in R grapheme 3 and impediment A be an
> essential in R grapheme 3 orthgonal to both B and C. Use fly algebra to
> test A is equal to B irritable C.
>
> Hint: Find a basis. Please do not utilize consume agent compounents or easy vector
> algebra. Must employ linelike algebra techniques.
>
>
>
> Posted nearby acf to Maths,administration,counselling at 11:50 AM

R3 DIMENSION.
B AND C ARE NON PARALLEL.
HENCE THEY ARE INDEPENDENT VECTORS
A IS ORTHOGONAL TO BOTH B AND C.
HENCE A IS NEITHER DEPENDENT ON B NOR ON C.
HENCE A,B,C ARE 3 INDEPENDENT VECTORS IN R3
HENCE A,B,C FORM A BASIS IN R3
HENCE
B X C = xA+yB+zC
BUT
B X C IS PERPENDICULAR TO BOTH B AND C.
HENCE IT CAN NOT HAVE A COMPONENT ALONG B OR C...THAT IS ITS COMPONENTS ALONG B AND C ARE ZEROS
THAT IS
y=z=0
HENCE
B X C = xA
HENCE
B X C AND A ARE DEPENDENT ....COLLINEAR OR PARALLEL VECTORS.