If `x = cy + bz, y = az + cx,z = bx + ay` where `x,y,z` are not all zero, prove that `a^2 + b^2 + c^2 + 2ab = 1.`

Given a = x/(y - z), b = y/(z - x) and c = z/(x - y) , where x,y and z are not all zero, Then the value of ab + bc + ca a)0 b)1 c)-1 d)None of these

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 the equation of the sphere through the circle x ^(2) +y ^(2) + z ^(2) = 9, 2x + 3y + 4z = 5 and through the point (1,2,3) is 3 (x ^(2) + y ^(2) + z ^(2)) - 2x - 3y - 4z = C, then the value of C is

If x=1 +a + a^2+…. to oo , where |a| lt1 and y=1+b+b^2+… to oo , where |b|lt1 , prove that 1+ab+a^2b^2+… to oo=((xy)/(x+y-1))

y=e^(ax)sin bx : Prove that y_2-2ay_1+(a^2+b^2)y=0 .

If a, b, c are in AP and a^(1/x)=b^(1/y)=c^(1/z) prove that x, y, z are in AP.

Value of |(x+y,z,z),(x,y+z,x),(y,y,z+x)| where x , y ,z are non - zero real number is equal to a)xyz b)2xyz c)3xyz d)4xyz

If a,b,c,d,e and f are in GP, then the value of determinant |{:(a ^(2) , d ^(2) , x), ( b ^(2) , e^(2), y) , (c^(2) , f^(2), z}| depends on a) x and y b) x and z c) y and z d) independent of x,y,z

If the equation of the sphere through the circle and the plane x ^(2) + y ^(2) + z^(2) = 5, 2x + 3y + 4z = 5 and through the origin is x ^(2) + y ^(2) + z ^(2) - 2x - 3y - 4z + c =0 .Then value of c is