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Show that veca.(vecbxxvec c) is equal in magnitude to the volume of the parallelopiped formed on the three vectors, veca,vecb and vec c

Answer» <html><body><p></p>Solution :Suppose `<a href="https://interviewquestions.tuteehub.com/tag/vec-723433" style="font-weight:bold;" target="_blank" title="Click to know more about VEC">VEC</a>(OA)=vecb,vec(OC)=vecc and vec(OE)=<a href="https://interviewquestions.tuteehub.com/tag/veca-3257210" style="font-weight:bold;" target="_blank" title="Click to know more about VECA">VECA</a>` `vecb and vec c` are adjacent sides of parallelogram OABC <br/> Area of `squareOABC,vecS=vecbxxvecc` <br/> `:.Shatn=vecbxxvecc` <br/> where `<a href="https://interviewquestions.tuteehub.com/tag/hatn-2693621" style="font-weight:bold;" target="_blank" title="Click to know more about HATN">HATN</a>` unit vector perpendicular to plane form by `vecb and vecc and theta` is angle between `veca and vecS`. <br/> `:.veca.(vecbxxvecc)=veca.vecS [because vecbxxvecc=vecS]` <br/> `=aScostheta` <br/> `=(acostheta)S` <br/> `=hS""......(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)` <br/> where in `DeltaEOE., EE.=h=acostheta` <br/> Suppose <a href="https://interviewquestions.tuteehub.com/tag/volume-728707" style="font-weight:bold;" target="_blank" title="Click to know more about VOLUME">VOLUME</a> of parallelepiped OABCDEF is V. <br/> `:.V` = Area of `squareOABCxx` perpendicular (h) of parallelogram OABC from E <br/> `:. V=sh"".....(2)` <br/> From result (1) and (2) <br/> `veca.(vecbxxvecc)=V`</body></html>


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