If `l_(1), l_(2), l_(3)` are respectively the perpendicular from the vertices of a triangle on the opposite side, then show that `l_(1)l_(2) l_(3) =(a^(2)b ^(2) c^(2))/(8R^(3)).`

If l, l_(1), l_(2) and l _(3) be respectively the radii of the in-circle and the three escribed circles of a Delta ABC, then find l_(1)l_(2) l_(3)-l(l_(1)l_(2) +l_(2) l_(3)+l_(1) l_(3)).

If l_(1),l_(2),l_(3) are the lengths of the emitter, base and collector of a transistor then

Let position vectors of point A,B and C of triangle ABC represents be hati+hatj+2hatk, hati+2hatj+hatk and 2hati+hatj+hatk . Let l_(1),l_(2) and l_(3) be the length of perpendicular drawn from the orthocenter 'O' on the sides AB, BC and CA, then (l_(1)+l_(2)+l_(3)) equals

If l_(3)andl_(2) represent angular momenta of an orbiting electron in III and II Bohr orbits respectively, then l_(3):l_(2) is :

Let position vectors of point A,B and C of triangle ABC represents be hati+hatj+2hatk, hati+2hatj+hatk and 2hati+hatj+hatk . Let l_(1)+l_(2) and l_(3) be the length of perpendicular drawn from the orthocenter 'O' on the sides AB, BC and CA, then (l_(1)+l_(2)+l_(3)) equals

If l_(1), m_(1), n_(1), l_(2), m_(2), n_(2) and l_(3), m_(3), n_(3) are direction cosines of three mutuallyy perpendicular lines then, the value of |(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3))| is

Consider atoms H, He^(+), Li^(++) in their ground states. If L_(1), L_(2) and L_(3) are magnitude of angular momentum of their electrons about the nucleus respectively then: A. L_(1)=L_(2)=L_(3) B. L_(1) gt L_(2) gt L_(3) C. L_(1) lt L_(2) lt L_(3) D. L_(1)=L_(2)=L_(3)

If l_(1), m_(1), n_(1) and l_(2),m_(2),n_(2) are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1) .

If l_(1), m_(1), n_(1) and l_(2),m_(2),n_(2) are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1) .

If l_(1),l_(2) and l_(3) are the orders of the currents through our nerves, domestic appliances and average lightening, then the correct order of currents is (1) l_(1) gt l_(2) gt l_(3) (2) l_(1) gt l_(3) gt l_(2) (3) l_(1) lt l_(2) lt l_(3) (4) l_(1) = l_(2) = l_(3)