Find the values of x such that the given vectors are orthogonal. (Enter your answers from smallest to largest.)
xi + 3xj
xi - 5j
x = _______ (smaller value)
x = _______ (larger value)
The answer is 0 and 15, but how do I get that?
Find the values of x such that the given vectors are orthogonal. (Enter your answers from smallest to largest.)
xi + 3xj
xi - 5j
x = _______ (smaller value)
x = _______ (larger value)
The answer is 0 and 15, but how do I get that?
Let's consider the two vectors as two complex numerrs...
$\displaystyle z_{1} = x + 3 x i$
$\displaystyle z_{2} = x - 5i$
... where $\displaystyle i = \sqrt{-1}$ is the 'imaginary unit'. The condition of orthogonality is...
$\displaystyle Re\{\frac{z_{1}}{z_{2}}\} = 0$
... that leads at the algebraic equation...
$\displaystyle x^{2} - 15 x=0$
... whose solution are $\displaystyle x=0$ and $\displaystyle x=15$ ...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$