Dane są wektory \(\displaystyle{ \vec{a} = [3,−2, 1]}\), \(\displaystyle{ \vec{b} = [1, 2, 1]}\), \(\displaystyle{ \vec{c} = [−1, 4, 3]}\). Obliczyć:
\(\displaystyle{ [(\vec{b} \circ \vec{c})(2\vec{c} \times \vec{a})] \circ [(\vec{a}-\vec{b}) \times (\vec{a}+\vec{c})]}\)
\(\displaystyle{ \vec{b} \circ \vec{c}=1+8+3=12}\)
\(\displaystyle{ 2\vec{c} \times \vec{a}=(-4,16,-20)}\)
\(\displaystyle{ (\vec{b} \circ \vec{c})(2\vec{c} \times \vec{a})=(24,84,-240)}\)
\(\displaystyle{ \vec{a}-\vec{b}=(2,0,0)}\)
\(\displaystyle{ \vec{a}+\vec{b}=(4,6,4)}\)
\(\displaystyle{ (\vec{a}-\vec{b}) \times (\vec{a}+\vec{c})=(0,-8,12)}\)
\(\displaystyle{ [(\vec{b} \circ \vec{c})(2\vec{c} \times \vec{a})] \circ [(\vec{a}-\vec{b}) \times (\vec{a}+\vec{c})]=(0,-672,-2880)}\)
Czy jest to dobrze zrobione?