InterviewSolution
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InterviewSolution
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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. `1/3`B. `4`C. `(3sqrt(3))/4`D. `4/(3sqrt(3))` |
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Answer» Correct Answer - B Let `veca=hati+hatj, vecb=hatj+hatk, vecc=hatk+hati` Let `vecn_(1),vecn_(2),vecn_(3)` be the normals to the given planes. Then, `vecn_(1)=vecaxxvecb, vecn_(2)=vecbxxvecc` and `vecn_(3)=veccxxveca` `:.` Volume of the given parallelopiped is given by `[(vecn_(1), vecn_(2), vecn_(3))]=[(veca, vecb, vecc)]^(2)=|(1, 1, 0),(0, 1,1),(1,0, 1)|^(2)=4` |
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