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| 1. |
Find the cross product a=2i+3j+k & b= I-j+2k |
| Answer» {tex}\\eqalign{ & {\\rm{Here,}}\\vec a = 2\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over i} + 3\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over j} + \\hat k \\cr & {\\rm{ }}\\vec b = \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over i} - \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over j} + 2\\hat k \\cr & {\\rm{ \\vec a \\times \\vec b = }}\\left| {\\matrix{ {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over i} } & {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over j} } & {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over k} } \\cr 2 & 3 & 1 \\cr 1 & { - 1} & 2 \\cr } } \\right| \\cr & = \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over i} \\left[ {3 \\times 2 - 1 \\times ( - 1)} \\right] - \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over j} \\left[ {2 \\times 2 - 1 \\times (1)} \\right] + \\hat k\\left[ {2 \\times ( - 1) - 3 \\times 1} \\right] \\cr & = 7\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over i} - 3\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over j} - 5\\hat k \\cr} {/tex} | |