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 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_(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)

In the network in given find l_(1), l_(2) and l.

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

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

Let L_(1),L_(2),L_(3) be three straight lines a plane and n be the number of circles touching all the lines . Find the value of n.

The direction cosines of a line equally inclined to three mutually perpendiclar lines having direction cosines as l_(1),m_(1),n_(1),l_(2),m_(2),n_(2) and l_(3), m_(3),n_(3) are

Two rods, one of aluminium and other made of steel, having initial lengths l_(1) and l_(2) are connected together to form a single rod of length (l_(1)+l_(2)) . The coefficient of linear expansions for aluminium and steel are alpha_(a) and alpha_(s) respectively. If length of each rod increases by same amount when their tempertures are raised by t^(@)C , then find the ratio l_(1) (l_(1)+l_(2)) .

A=[{:(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)):}] and B=[{:(p_(1),q_(1),r_(1)),(p_(2),q_(2),r_(2)),(p_(3),q_(3),r_(3)):}] Where p_(i), q_(i),r_(i) are the co-factors of the elements l_(i), m_(i), n_(i) for i=1,2,3 . If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) and (l_(3),m_(3),n_(3)) are the direction cosines of three mutually perpendicular lines then (p_(1),q_(1), r_(1)),(p_(2),q_(2),r_(2)) and (p_(3),q_(),r_(3)) are