If `z=(lambda+3)+isqrt(5-lambda^2)` then the locus of Z is

A system of equations lambdax +y +z =1,x+lambday+z=lambda, x + y + lambdaz = lambda^2 have no solution then value of lambda is

If x + y + z =a and the minimum value of a/x+a/y+a/z is 81^lambda , then the value of . lambda is

If A,B,C are three points in the Argand plane representing the complex numbers, z_(1),z_(2),z_(3) such that z_(1)=(lambdaz_(2)+z_(3))/(lambda+1) , where lambda in R , then the distance of A from the line BC, is

If the lines (x-1)/(2)=(y)/(-1)=(z)/(2) and x-y+z-2=0=lambdax+3z+5 are coplanar, then the value of 7lambda is equal to

Two lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=(z)/(1) intersect at a point P. If the distance of P from the plane 2x-3y+6z=7 is lambda units, then the value of 49lambda is equal to

If the matrix A = [[lambda_(1)^(2), lambda_(1)lambda_(2), lambda_(1) lambda_(3)],[lambda_(2)lambda_(1),lambda_(2)^(2),lambda_(2)lambda_(3)],[lambda_(3)lambda_(1),lambda_(3)lambda_(2),lambda_(3)^(2)]] is idempotent, the value of lambda_(1)^(2) + lambda_(2)^(2) + lambda _(3)^(2) is

Let z be a complex number. If the minimum value of |z|^2+|z-3|^2+|z-3i|^2 is lambda , then the value of 6lambda is (1) 23 (2) 42 (3) 72 (4) 84

If the origin and the non - real roots of the equation 3z^(2)+3z+lambda=0, AA lambda in R are the vertices of an equilateral triangle in the argand plane, then sqrt3 times the length of the triangle is

Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-5y+4z=lambda is consistent and find the solutions for all such values of lambdadot

The Cartesian equation of the plane vec r=(1+lambda-mu) hat i+(2-lambda) hat j+(3-2lambda+2mu) hat k is a. 2x+y=5 b. 2x-y=5 c. 2x+z=5 d. 2x-z=5