InterviewSolution
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InterviewSolution
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Read the following passage and answer the questions. Consider the lines `L_(1):(x+1)/(3)=(y+2)/(1)=(z+1)/(2),L_(2):(x-2)/(1)=(y+2)/(2)=(z-3)/(3)` The unit vector perpendicualr to both `L_(1)` and `L_(2)` isA. `1/(sqrt(99))(-hati+7hatj+7hatk)`B. `1/(5sqrt(5))(-hati-7hatj+5hatk)`C. `1/(5sqrt(3))(-hati+7hatj+5hatk)`D. `1/(sqrt(99))(7hati-7hatj-hatk)` |
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Answer» Correct Answer - B Lines `L_(1)` and `L_(2)` are parallel to the vectors `vecb_(1)=3hati+hatj+2hatk` and `vecb_(2)=hati+2hatj+3hatk` respectively. Therefore, a unit vector perpendicular to both `L_(1)` and `L_(2)` is `hatn=(vecb_(1)xxvecb_(2))/(|vecb_(1)xxvecb_(2)|)` Now `vecb_(1)xxvecb_(2)=|(hati,hatj,hatk),(3,1,2),(1,2,3)|=-hati-7hatj+6hatk` `:.hatn=1/(5sqrt(3))(-hati-7hatj+5hatk)` |
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