InterviewSolution
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InterviewSolution
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the lines `(x-2)/1` = `(y-3)/1` = `(z-4)/-k` and `(x-1)/k` = `(y-4)/1` = `(z-5)/1` are coplanar if k=?A. any valueB. exactly one valueC. exactly two valuesD. exactly three values |
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Answer» Correct Answer - C Condition for two lines are coplanar. `|{:(x_(1)-x_(2),y_(1)-y_(2),z_(1)-z_(2)),(" "l_(1)," "m_(1)," "n_(1)),(" "l_(2)," "m_(2)," "n_(2)):}|=0` where, `(x_(1), y_(a), z_(1))` and `(x_(2), y_(2), z_(2))` are the points lie on lines (i) and (ii) respectively and `ltl_(1), m_(1), n_(1)gt` and `ltl_(2), m_(2), n_(2)gt` are the dirction cosines of the lines (i) and (ii), respectively. `:." "|{:(2-1,3-4,4-5),(" "1," "1," "-k),(" "k," "2," "1):}|=0` `implies" "|{:(1,-1," "-1),(1," "1," "-k),(k," "2," "1):}|=0` `implies1(1+2k)+(1+k^(2))-(2-k)=0` `implies" "k^(2)+2k+k=0` `implies" "k^(2)+3k=0` `implies" "k=0,-3` If 0 appears in the denominator, then the correct way of representing the equation of straight line is `(x-2)/(1)=(y-3)/(1),z=4` |
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