If `B'=[x y z], B=|[x y z]|` and `A=|[0,3,3],[-3,0,4],[-3,-4,0]|` then `B'AB`=

If xneynez and |[x,x^3,x^4-1],[y,y^3,y^4-1],[z,z^3,z^4-1]|=0 , then prove that : xyz(xy+yz+zx)=x+y+z

If x+y+z=0 show that x^3+y^3+z^3=3x y z .

If the system of equations x - 2y +z = a , 2x + y - 2z = b, x +3y - 3z = c, has at least one solution, then a) a + b + c = 0 b) a - b + c = 0 c) -a + b + c = 0 d) a + b - c = 0

If a,x,b are in A.P.,a,y,b are in G.P. and a,z,b are in H.P. such that x=9z and a>0, b>0, then (a) y=3z. (b) x=3y (c) 2y= x+z (d) none of these

If x =a, y=b, z=c is a solution of the system of linear equations x + 8y + 7z =0, 9 x + 2y + 3z =0, x + y+z=0 such that point (a,b,c ) lies on the plane x + 2y + z=6, then 2a+ b+c equals

If x =a, y=b, z=c is a solution of the system of linear equations x + 8y + 7z =0, 9 x + 2y + 3z =0, x + y+z=0 such that point (a,b,c ) lies on the plane x + 2y + z=6, then 2a+ b+c equals

Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z-4 and is parallel to the line of intersection of the planes 2x + 3y +z=1 and x + 3y + 2z = 2 be x + Ay + Bz + C=0 Compute the value of |A+B+C| .