[(m+n)^(2)quad J^(2)quad mn],[23.([(n+1)^(2),m^(2),in],[(7+m)^(2),n^(2),6n])=(l^(2)+m^(2)+n^(2))(1-m)(m-n)(n-1)]

|[(m+n)^(2), l^(2), mn], [(n+l)^(2), m^(2), ln], [(l+m)^(2), n^(2), lm]| =(l^(2) +m^(2) +n^(2))(l-m)(m-n)(n-l)(l+m+n)

Find the square root of (m^(n^(2))n^(m^(2))a^((m+n)))/((m+n)^((m+n)^(2) (i) (m^n)(n^m)a^((m+n)/2) (ii) ((m^(n^2))(n^(m^2))a^((m+n)/2))/(m+n)^(((m+n)^2)/2) (iii) (m^n)(n^m)a^(sqrt(m+n))/(m+n)^(((m+n))) (iv)none of these

Given sin alpha+sin beta=l,cos alpha+cos beta=mtan((alpha)/(2))tan((beta)/(2))=n,(A)(l^(2)+m^(2))(1-n)=2l(1+n)(B)(l^(2)+m^(2))(1+n)=2l(1-n)(C)(l^(2)+m^(2))(1-n)=2m(1+n)(D)(l^(2)+m^(2))(1+n)=2m(1-n)

If (m + n)/(m + 3n) = (2)/(3) , find : (2n^(2))/(3m^(2) + mn) .

If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) are d.c's of two lines then find the value of (l_(1)m_(2)-l_(2)m_(1))^(2)+(m_(1)n_(2)-n_(1)m_(2))^(2)+(n_(1)l_(2)-n_(2)l_(1))^(2)+(l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2))^(2)

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If the angle between the lines is 60^(@) then the value of l_(1)(l_(1)+l_(2))+m_(1)(m_(1)+m_(2))+n_(1)(n_(1)+n_(2)) is

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If the angle between the lines is 60^(@) then the value of l_(1)(l_(1)+l_(2))+m_(1)(m_(1)+m_(2))+n_(1)(n_(1)+n_(2)) is

If the direction cosines of two lines are l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) , then find the direction cosine of a line perpendicular to these lines. a) l_(1)+l_(2),m_(1)+m_(2),n_(1)+n_(2) b) l_(1)-l_(2),m_(1)-m_(2),n_(1)-n_(2) c) m_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1) d) l_(1)+2l_(2),m_(1)+2m_(2),n_(1)+2n_(2)