A unit vector perpendicular to the lines r¯$$=($$−i¯−$$2j$$¯−k¯$$)+t(3i$$¯$$+j$$¯$$+2k$$¯$$)$$ , $$r=(2i$$¯−$$2j$$¯$$+3k$$¯$$)+s(i$$¯$$+2j$$¯$$+3k$$¯$$)$$ where s∈R,t∈R , is

Correct option is 3−i¯−7j¯+5k¯53

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$A unit vector perpendicular to the lines \bar{r} = (- \bar{i} - 2 \bar{j} - \bar{k}) + t (3 \bar{i} + \bar{j} + 2 \bar{k}), r = (2 \bar{i} - 2 \bar{j} + 3 \bar{k}) + s (\bar{i} + 2 \bar{j} + 3 \bar{k}) where s \in R, t \in R, is$

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−i¯+7j¯+5k¯53

7i¯−7j¯−k¯311

−i¯−7j¯+5k¯53

−i¯+7j¯+7k¯311

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detailed solution

Correct option is C

ijk312123=i¯−1−j¯7+k¯5=−i¯−7j¯+5k¯ Unit vector =−i¯−7j¯+5k¯1+49+25

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A unit vector perpendicular to the lines r¯=(−i¯−2j¯−k¯)+t(3i¯+j¯+2k¯) , r=(2i¯−2j¯+3k¯)+s(i¯+2j¯+3k¯) where s∈R,t∈R , is

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$A unit vector perpendicular to the lines \bar{r} = (- \bar{i} - 2 \bar{j} - \bar{k}) + t (3 \bar{i} + \bar{j} + 2 \bar{k}), r = (2 \bar{i} - 2 \bar{j} + 3 \bar{k}) + s (\bar{i} + 2 \bar{j} + 3 \bar{k}) where s \in R, t \in R, is$