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Find the value of \(\rm \hat{i} \times \hat{i} = \hat j \times \hat j = \hat k \times \hat k\)

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Correct Answer - Option 1 : 0

Concept:

Dot product of two vectors is defined as:

\({\rm{\vec A}}{\rm{.\vec B = }}\left| {\rm{A}} \right|{\rm{ \times }}\left| {\rm{B}} \right|{\rm{ \times cos}}\;{\rm{\theta }}\)

Cross/Vector product of two vectors is defined as:

\({\rm{\vec A \times \vec B = }}\left| {\rm{A}} \right|{\rm{ \times }}\left| {\rm{B}} \right|{\rm{ \times sin}}\;{\rm{\theta }} \times \rm \hat{n}\)

where θ is the angle between \({\rm{\vec A}}\;{\rm{and}}\;{\rm{\vec B}}\)

Calculation:

To Find: Value of \(\rm \hat{i} \times \hat{i}\)

Here angle between them is 0°

\({\rm{\hat i \times \hat i = }}\left| {\rm{i}} \right|{\rm{ \times }}\left| {\rm{i}} \right|{\rm{ \times sin}}\;{\rm{0 }} \times \rm \hat{n}=0\)

Similarly \(\rm \hat j \times \hat j = \hat k \times \hat k = 0\)

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