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Write the Value of ^ I . ( ^ J × ^ K ) + ^ J . ( ^ K × ^ I ) + ^ K . ( ^ J × ^ I ) . - Mathematics

Short Note

Write the value of  \[\hat{ i } . \left( \hat{ j } \times \hat{ k }  \right) + \hat{ j }  . \left( \hat{ k } \times \hat{ i }  \right) + \hat{ k }  . \left( \hat{ j }  \times \hat{ i }  \right) .\]

 

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Solution

\[\hat{ i } . \left( \hat{ j } \times \hat{ k } \right) + \hat{ j } . \left( \hat{ k } \times \hat{ i }  \right) + \hat{ k }  . \left( \hat{ j }  \times \hat{ i } \right)\]
\[ = \hat{ i }  . \hat{ i}  + \hat{ j} . j + \hat{ k }  . \left( - \hat{ k } \right)\]
\[ = \left| \hat{ i } \right|^2 + \left| \hat{ j }  \right|^2 - \left| \hat{ k }  \right|^2 \]
\[ = 1 + 1 - 1 ( \because \left| \hat{ i }  \right| = 1, \left| \hat{ j } \right| = 1 \text{ and }  \left| \hat{ k }  \right| = 1)\]

\[ = 1\]

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APPEARS IN

RD Sharma Class 12 Maths
Chapter 25 Vector or Cross Product
very short answers | Q 3 | Page 33
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