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

If x=c y+b z ,y=a z+c x ,z=bx+a y ,w h e r ex ,y ,z are not all zeros, then find the value of a^2+b^2+c^2+2a b c dot

If a^x=b ,b^y=c ,c^z=a , then find the value of x y zdot

If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero solution, then the possible value of k are -1,2 b. 1,2 c. 0,1 d. -1,1

If the circles x^2+y^2+2a x+c y+a=0 and x^2+y^2-3a x+d y-1=0 intersects at points P and Q , then find the values of a for which the line 5x+b y-a=0 passes through Pa n dQdot

If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite solutions, then the value of equation has no solution is -3 b. 1 c. 0 d. 3

The value of k for which the planes kx+4y+z=0, 4x+ky+2z=0 nd 2x+2y+z=0 intersect in a straighat line is (A) 1 (B) 2 (C) 3 (D) 4

Given a=x//(y-z), b=y//(z-x),a n dc=z//(x-y),w h e r ex , y , za n dz are not all zero, then the value of a b+b c+c a is 0 b. 1 c. -1"" d. none of these

If p q r!=0 and the system of equation (p+a)x+b y+c z=0 a x+(q+b)y+c z=0 a x+b y+(r+c)z=0 has nontrivial solution, then value of a/p+b/q+c/r is -1 b. 0 c. 0"" d. not-2

If p q r!=0 and the system of equation (p+a)x+b y-c z=0 a x+(q+b)y+c z=0 a c+b y+(r+c)z=0 has nontrivial solution, then value of 1/p+b/q+c/r is -1 b. 0 c. 0"" d. not-2

If the parabola y=(a-b)x^2+(b-c)x+(c-a) touches x- axis then the line ax+by+c=0 passes through a fixed point