Question

If |x|=11, |y|=23 and |x-y|=30, find |x+y|, x and y are vectors

Answer 1

\[\left| x-y \right|^2=\left( x-y \right)^2=\left( x-y \right).\left( x-y \right)\]
\[=x.x-x.y-y.x+y.y (x.y=y.x)\]
\[=x^2-2x.y+y^2=\left| x \right|^2-2 x.y+\left| y^2 \right|=\left( 11 \right)^2+\left( 23 \right)^2-2 x.y\]
\[\left( 30 \right)^2-\left( 11 \right)^2-\left( 23 \right)^2=-2x.y\]
\[2 x.y=121+529-900=-250\]
\[\left| x+y \right|^2=\left( x+y \right)^2=\left( x+y \right).\left( x+y \right)=?\]
Then find \[\left| x+y \right|\]

Answer 2

Yes ^