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If position vector of the points $A,B,C,D$ are given by $7\hat i-4\hat j+7\hat k,\:\hat i-6\hat j+10\hat k,\:-\hat i-3\hat j+4\hat k\:\:and\:\:5\hat i-\hat j+5\hat k$ respectively, then $ABCD$ is ?

$(a)\:\:Rhombus\:\:\:\qquad\:\:(b)\:\:Rectangle\:\:\:\qquad\:\:(c)\:\:Parallelogram\:\: but\:\: not \:\:Rhombus\:\:\:\qquad\:\:(d)\:\:None\:\:of\:\:these.$

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1 Answer

$\overrightarrow {AB}=-6\hat i-2\hat j+3\hat k$, $\overrightarrow {AC}=-8\hat i+\hat j-3\hat k$, $\overrightarrow {AD}=-2\hat i+3\hat i-2\hat k$
$\overrightarrow {BC}=-2\hat i+3\hat j-6\hat k$ $\overrightarrow{BD}=4\hat i+5\hat j-5\hat k$ and $\overrightarrow {CD}=6\hat i+2\hat j+\hat k$
Since $\overrightarrow {AB}$ is not parallel to $\overrightarrow {CD}$ and $\overrightarrow {BC}$ is not parallel to $\overrightarrow {AD}$,
$ABCD$ is none of the above figures.
answered Dec 30, 2013 by rvidyagovindarajan_1

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