Solve for `a, lambda,` if `log_lambda a * log_5 lambda * log_lambda 25 = 2.`

The d.r.s of two perpendicular lines are 1,-3,5 and lambda,1 + lambda,2 + lambda then lambda is

det [[lambda ^ (4) +2 lambda ^, 2 lambda ^ (3) -3,3 lambda ^ (2) + lambda2,3,15,0,2]] = a lambda ^ (4) + b lambda ^ (3) + c lambda ^ (2) + d lambda + e

p(lambda)^4+q(lambda)^3+r(lambda)^2+s(lambda)+t = |((lambda^2 + 3lambda) , lambda -1 , lambda+3) , (lambda +1 , -2lambda , lambda-4 ) ,(lambda-3 , lambda+4 , 3lambda)| find t=?

Show that the area of the triangle with vertices (lambda, lambda-2), (lambda+3, lambda) and (lambda+2, lambda+2) is independent of lambda .

Show that the area of the triangle with vertices (lambda, lambda-2), (lambda+3, lambda) and (lambda+2, lambda+2) is independent of lambda .

Show that the area of the triangle with vertices (lambda, lambda-2), (lambda+3, lambda) and (lambda+2, lambda+2) is independent of lambda .

Show that the area of the triangle with vertices (lambda, lambda-2), (lambda+3, lambda) and (lambda+2, lambda+2) is independent of lambda .

Transition between three energy energy levels in a particular atom give rise to three Spectral line of wevelength , in increasing magnitudes. lambda_(1), lambda_(2) and lambda_(3) . Which one of the following equations correctly ralates lambda_(1), lambda_(2) and lambda_(3) ? lambda_(1)=lambda_(2)-lambda_(3) lambda_(1)=lambda_(3)-lambda_(2) (1)/(lambda_(1))=(1)/(lambda_(2))+(1)/(lambda_(3)) (1)/(lambda_(2))=(1)/(lambda_(3))+(1)/(lambda_(1))