1.

The direction cosines of aline satisfy the relations `lambda(l+m)=na n dm n+n l+l m=0.`The value of `lambda,`for which the two lines are perpendicular toeach other, isa. `1`b. `2`c. `1//2`d. noneof theseA. 1B. 2C. `1//2`D. none of these

Answer» Correct Answer - b
Eliminating `n`, we get
`" "lamda(l+m)^(2)+lm=0`
`rArr" "(lamdal^(2))/(m^(2))+ (2lamda+1)(l)/(m) + lamda=0`
`rArr" "(l_1l_2)/(m_(1)m_(2))=1" "` (product of roots `(l_1)/(m_1) and (l_2)/(m_2)` )
where `l_1//m_1 and l_2//m_2` are the roots of this equation, further eliminating m, we get
`" "lamdal^(2)-ln-n^(2)=0`
`rArr" "(l_(1)l_(2))/(n_(1)n_(2))=-(1)/(lamda)`
Since the lines with direction cosines `(l_1, m_1, n_1) and (l_2, m_2, n_2)` are perpendicular, we have
`" "l_1l_2+ m_1m_2 + n_1n_2 = 0`
or `" "1+1-lamda=0`
or `" "lamda=2`


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