मान ज्ञात करें : (2i + 3j + 4k). (3i - 7j + 8k) x (5i - 4j + 12k)

Question

मान ज्ञात करें : \((2 \vec{i}+3 \vec{j}+4 \vec{k}) \cdot(3 \vec{i}-7 \vec{j}+8 \vec{k}) \times(5 \vec{i}-4 \vec{j}+12 \vec{k})\)

Answer 1

Let \(\vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}, \vec{b}=3 \hat{i}-7 \hat{j}+8 \hat{k}, \vec{c}=5 \hat{i}-4 \hat{j}+12 \hat{k}\)

\(\therefore \vec{a} \cdot(\vec{b} \times \vec{c})=[\vec{a} \vec{b} \vec{c}] \)

\( =\left|\begin{array}{rrr} 2 & 3 & 4 \\ 3 & -7 & 8 \\ 5 & -4 & 12 \end{array}\right| \)

\(= 2(-84+32)-3(36-40)+4(-12+35) \)

\( =2(-52)-3(-4)+4(23)\)

\(=-104+12+92=-104+104= 0\)