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The three vectors `hati+hatj, hatj+hatk, hatk+hati` taken two at a time form three planes. The three unit vectors drawn perpendicular to these three planes form a parallelopiped of volume.A. 43468B. 4C. `(3 sqrt(3)) 4`D. `4//(3sqrt(3))` |
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Answer» Correct Answer - C `Let [{:(veca=hati+hatj),(vecb=hatj+hatk),(vecc=hatk+hati):}` `hatr_(1)=((vecaxxvecb))/(|vecaxxvecb|)=((hati-hatj+hatk))/(sqrt(3))` `Similarly , hatr_(2)=((vecbxxvecc))/(|vecbxxvecc|)=(1)/(sqrt(3))(hati+hatj-hatk)` ` hatr_(3)=((vecbxxvecc))/(|vecbxxvecc|)=(1)/(sqrt(3))(-hati+hatj+hatk)` then , the required Volume is `impliesV=(1)/(3sqrt(3))|{:(1,-1,1),(1,1,-1),(-1,1,1):}|=(4)/(3sqrt(3))` |
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