The distance between the plane `x-2y+z-6=0` and the plane containing the sets of points `(1+2 lambda,2+3 lambda,3+4 lambda)` and `(2+3 mu,3+4 mu,4)` are parameters is

If the distance between the plane 23x-10y-2z+48 =0 and the plane containing the lines (x+1)/2 =(y-3)/4= (z+1)/(3) and (x+3)/(2)=(y+2)/6 = (z-1)/(lambda)(lambda in R) is equal to k/sqrt(633) , then k is equal to __________.

Find the values of lambda ad mu if the points A(-1,4,-2),B(lambda,mu,1) and C(0,2,-1) are collinear.

The plane 2x-(1+lambda)y+3 lambda z=0 passes through the intersection of the plane

If the angle between the line x=(y-1)/(2)=(z-3)(lambda) and the plane x+2y+3z=4 is cos^(-1)(sqrt((5)/(14))) , then lambda equals

The plane 2x-2y+z+12=0 touches the surface x^2+y^2+z^2-2x-4y+2z-3=0 only at point (-1, lambda, -2) . The value of lambda must be

If the points (0,1,-2),(3,lambda,-1) and (mu,-3,4) are collinear,then the value of lambda and mu are given by

For which value of lambda , plane 4x + 6y -2z =8 and 2x+3y+ lambda z= 12 are parallel?