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If $\overrightarrow a=\hat i-\hat k,\:\overrightarrow b=x\hat i+\hat j+(1-x)\hat k\:and\:\overrightarrow c=y\hat i+x\hat j+(1+x-y)\hat k$, then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]$ depends on?

$\begin{array}{1 1} Only \;x \\ Only \;y \\ neither\;x \;nor\;y \\ both\;x\;and\;y \end{array} $

1 Answer

$[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]$$=\begin{vmatrix}1& 0&-1\\x &1 &1-x\\y &x &(1+x-y)\end {vmatrix}$
which is independent of $x\:and\:y$
answered Nov 4, 2013 by rvidyagovindarajan_1

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