If a - - - - - k- b - - - - - k- - c - - - - - k- then

For a=i+j+k;b=i j+k;c=i+j k A) a· b+b· c+c· a=( 1 ) +( 1 ) +( 1 ) =1 B) ( ( a· c ) c+( c· b ) a ) · b=( ( 1 ) c+( 1 ) a ) · b=( c b ) · b=c· b ...

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Applications of Dot Product

If a = î + ...

Question

If $\to a =^i +^j +^k; \to b =^i -^j +^k; \to c =^i +^j -^k$ , then

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Solution

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\to a =^i +^j +^k

\to b =^i +^j -^k

\to c =^i -^j +^k

\to d =^i -^j -^k

| (\to a \times \to b) . (\to c \times \to d) | =

^i \times (^j \times^k) +^j \times (^k \times^i) +^k \times (^i \times^j) =

\to a =^i +^j +^k, \to b =^i +^j -^k

\to c =^i -^j +^k

\to d =^i -^j -^k

(\to a \times \to b) \times (\to c \times \to d) =

\to a =^i +^j +^k

\to b =^i -^j +^k

\to c =^i +^j -^k

\to a =^i -^j -^k

(\to a \times \to b) \times (\to c \times \to d)

\sqrt{2}

\to a =^i +^j + 2^k

\to b =^i + 2^j +^k

\to c =^i +^j +^k

-^i -^k

^j -^k

^i -^j

^i +^k

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