If the planes `x-cy-bz=0, cx-y+az=0 and bx+ay-z=0` pass through a line, then the value of `a^2+b^2+c^2+2abc` is

If the planes x-c y-b z=0,c x=y+a z=0a n db x+a y-z=0 pass through a straight line, then find the value of a^2+b^2+c^2+2a b cdot

If the planes x-c y-b z=0,c x=y+a z=0a n db x+a y-z=0 pass through a straight line, then find the value of a^2+b^2+c^2+2a b cdot

The planes ax+4y+z=0,2y+3z-1=0 and 3x-bz+2=0 will

If the three planes x=5,2x-5ay+3z-2=0 and 3bx+y-3z=0 contain a common line, then (a,b) is equal to

If 4x-ay+3z=0, x+2y+az=0 and ax+2z=0 have a non - trivial solution, then the number of real value(s) of a is

The variable plane x+3y+z-4+lambda(2x-y)=0 always passes through the line

If the equations ax^2+bx+c=0 and cx^2+bx+a=0, a!=c have a negative common root then the value of a-b+c=

Show that in general there are three values of t for which the following system of equations has a non- trival solution (a-t)x+by+cz=0, bx+(c-t)y+az=0 and cx+ay+(b-t)z=0. Express the product of these values of t in the form of a determinant.

The greatest value of for which the system of linear equations x-cy-cz=0 cx-y+cz=0 cx+cy-z=0 Has a non-trivial solution, is 1/k . The value of k is _________.

Given planes P_1:cy+bz=x P_2:az+cx=y P_3:bx+ay=z P_1, P_2 and P_3 pass through one line, if