L(1,2),M(5,3),N(8,6)

Find the centroid of tetrahedron with vertices K(5, -7, 0), L(1, 5, 3), M(4, -6, 3), N(6, -4, 2) ?

If A = [[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]] then Find A+I

If A = [[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]] then Find A+I

If A = [[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]] then Find A+I

Show that the matris [[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]] is orthogonal, if l_(1)^(2) + m_(1)^(2) + n_(1)^(2) = Sigmal_(1)^(2) = 1 = Sigma l_(2)^(2) = Sigma_(3) ^(2) and l_(1) l_(2) + m_(1)m_(2) + n_(1) n_(2) = Sigma l_(1)l_(2) =0 = Sigma l_(2)l_(3) = Sigma l_(3) l_(1).

The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. Do any of these combination have same energy. {:(1.,n=4,l=2,m_(l) = -2,m_(s)=-1//2,),(2.,n=3,l=2,m_(l) = 1,m_(s) = +1//2,),(3.,n=4,l=1,m_(l) = 0,m_(s) = +1//2,),(4.,n=3, l=2,m_(l) = -2,m_(s) = -1//2,),(5.,n=3,l=1,m_(l) = -1,m_(s) = +1//2,),(6.,n=4,l=1,m_(l) = 0,m_(s) = +1//2,):}

ABC is a right angled triangle in which /_B=90^(@) and BC=a. If n points L_(1),L_(2),"…….",L_(n) on AB are such that AB is divided in n+1 equal parts and L_(1)M_(1),L_(2)M_(2),"......,"L_(n)M_(n) are line segments parallel to BC and M_(1),M_(2),M_(3),"......,"M_(n) are on AC, the sum of the lenghts of L_(1)M_(1),L_(2)M_(2),"......,"L_(n)M_(n) is