LinAlg4.2.8

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If {\bar  {a}}=2{\bar  {i}}-3{\bar  {j}}+5{\bar  {k}},{\bar  {b}}=-{\bar  {i}}-4{\bar  {j}}+2{\bar  {k}}\,,then write {\bar  {a}}\times {\bar  {b}}\,

Given {\bar  {a}}=2{\bar  {i}}-3{\bar  {j}}+5{\bar  {k}},{\bar  {b}}=-{\bar  {i}}-4{\bar  {j}}+2{\bar  {k}}\,

{\bar  {a}}\times {\bar  {b}}={\begin{vmatrix}{\bar  {i}}&{\bar  {j}}&{\bar  {k}}\\2&-3&5\\-1&4&2\end{vmatrix}}\,

{\bar  {i}}(-6-20)-{\bar  {j}}(4+5)+{\bar  {k}}(8-3)=-26{\bar  {i}}-9{\bar  {j}}+5{\bar  {k}}\,


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