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Find the direction cosines of the two li...

Find the direction cosines of the two lines which are connected by the relations `l-5m+3n=0,7l^(2)+5m^(2)-3n^(2)=0`

Text Solution

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The correct Answer is:
`((-1)/(sqrt(6)),(1)/(sqrt(6)),(2)/(sqrt(6))),((1)/(sqrt(14)),(2)/(sqrt(14)),(3)/(sqrt(14)))`
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Find the direction cosines of two lines which are connected by the relations l-5m +3n = 0 and 7l^(2) +5m^(2)-3n^(2) = 0

Find the direction consines of two lines which are connected by the ralations l-5m+3n=0 and 7l^(2)+5m^(2)-3n^(2)=0

Knowledge Check

  • If the d.c's (l,m,n) of two lines are connected by the relations 7l^(2) + 5m^(2) - 3n^(2) = 0 , l - 5m + 3n = 0 then the d.c's of the two lines are

    A
    `((1)/(sqrt(6)),-(1)/(sqrt(6)),(1)/(sqrt(6))),((1)/(sqrt(6)),-(2)/(sqrt(6)),(1)/(sqrt(6)))`
    B
    `((1)/(sqrt(14)),-(2)/(sqrt(14)),(3)/(sqrt(6))),((1)/(sqrt(6)),(1)/(sqrt(6)),-(2)/(sqrt(6)))`
    C
    `((1)/(sqrt(14)),(2)/(sqrt(14)),(3)/(sqrt(14))),(-(1)/(sqrt(6)),(1)/(sqrt(6)),(2)/(sqrt(6)))`
    D
    `((1)/(sqrt(4)),(2)/(sqrt(4)),(3)/sqrt(4)),((-1)/(sqrt(3)),(1)/(sqrt(8)),(-2)/(sqrt(8)))`

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