# Compute the values

• December 11th 2007, 01:51 PM
akhayoon
Compute the values
for ||3X-4Y||

knowing that ||X||=2 AND ||Y||=1 and X.Y=-1

and then compute for

(3X+4Y).(X-5Y)

apparently the answer for the first is square root of 76

and the second is 1

I tried doing this the way the book tells me but I don't get the right answer at ALL!
• December 11th 2007, 02:29 PM
Plato
$\begin{array}{rcl}
\left\| {3X - 4Y} \right\|^2 & = & \left( {3X - 4Y} \right) \cdot \left( {3X - 4Y} \right) \\
& = & 9\left\| X \right\|^2 + 16\left\| Y \right\|^2 - 24\left( {X \cdot Y} \right) \\ \end{array}$

Just make the substitutions and the squareroot of both sides.