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 value(s) of lambda which satisfies the equation det[[1+lambda,2+lambda,-81,-1-lambda,2+lambda]]=0 is/are

If the points A(lambda, 2lambda), B(3lambda,3lambda) and C(3,1) are collinear, then lambda=

If the points A(lambda, 2lambda), B(3lambda,3lambda) and C(3,1) are collinear, then lambda=

If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists if lambda!=1 (b) lambda!=2 (c) lambda!=-1 (d) lambda!=0

If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists if (a) lambda!=1 (b) lambda!=2 (c) lambda!=-1 (d) lambda!=0

If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists if (a) lambda!=1 (b) lambda!=2 (c) lambda!=-1 (d) lambda!=0

If the vectors lambda i-3j+5k and 2 lambda i-lambda j-k are perpendicular to each other find 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))

The cartesian equation of the plane whose vector equation is r = (1 + lambda - mu) i + (2 - lambda) j + (3- 2 lambda + 2mu)k , where lambda, mu are scalars, is

If the rank of the matrix [(lambda,-1,0),(0, lambda,-1),(-1,0,lambda)] is 2, then find lambda .