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

Is there a real value of lambda for which the image of the point (lambda,lambda-1) by the line mirror 3 x + y = 6 lambda is the point (lambda^2 + 1, lambda) If so find lambda . ,

If the circumcentre of the triangle whose vertices are (3, 2, -5) , (-3, 8, -5) and (-3, 2, 1) is (-1, lambda, -3) the integer lambda must be equal to……

10 different vectors are lying on a plane out of which four are parallel with respect to each other. Probability that three vectors chosen from them will satisfy the equation lambda_1a+lambda_2b+lambda_3c=0, where lambda_1, lambda_2 and lambda_3ne=0 is

The Cartesian equation of the plane vec r=(1+lambda-mu) hat i+(2-lambda) hat j+(3-2lambda+2mu) hat k is

If lambda in R , then lambdaI_2 is the matrix

Let L_(1) -= ax+by+a root3 (b) = 0 and L_(2) -= bx - ay + b root3 (a) = 0 be two straight lines . The equations of the bisectors of the angle formed by the foci whose equations are lambda_(1)L_(1)-lambda_(2)L_(2)=0 and lambda _(1) l_(1) + lambda_(2) = 0 , lambda_(1) and lambda_(2) being non - zero real numbers ,are given by

Lambda_m^@ H_2O 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

The distance of the point (x,y) from the origin is defined as d = max . {|x|,|y|} . Then the distance of the common point for the family of lines x (1 + lambda ) + lambda y + 2 + lambda = 0 (lambda being parameter ) from the origin is

For what value of lambda , the vectors (lambda-2)veca+vecb and (4lambda-2)veca+3vecb are collinear