Q.

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

−i¯+7j¯+5k¯53

b

7i¯−7j¯−k¯311

c

−i¯−7j¯+5k¯53

d

−i¯+7j¯+7k¯311

answer is C.

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Detailed Solution

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