Problema Num. 3.
Dados los siguientes vectores: \(a=4i\ \vec{-}\ 3j\ +\ k\ \) y \(b=-i\ \vec{+}\ j+\ 4k\ \) Calcule \(\vec{a}\cdot\vec{b}\) y \(\vec{a\ }X\ \vec{b.}\)
\(\vec{a}=4i-3j+k\) \(\vec{b}=-i+j+4k\)
\(\left(a\right)\left(b\right)=4\left(-1\right)+\left(-3\right)\left(1\right)+\left(1\right)\left(4\right)\)
\(\left(a\right)\left(b\right)=-4-3+4\)
\(\left(a\right)\left(b\right)=3\)
\(i\) \(j\) \(k\)
\(4\) \(-3\) \(1\)
\(-1\) \(1\) \(4\)
\(a\ X\ b=\left[1\left(1\right)-\left(-3\right)\left(4\right)\right]-j\left[\left(4\right)\left(4\right)-\left(-1\right)\left(1\right)\right]+k\left[\left(4\right)\left(1\right)-\left(-1\right)\left(-3\right)\right]\)
\(a\ X\ b=i\left[1-\left(-12\right)\right]-j\left[16-\left(-1\right)\right]+k\left[4-3\right]\)
\(a\ X\ b=i\left(13\right)-j\left(17\right)+k\left(1\right)\)\(a\ X\ b=13i-17j+k\)