Let a, b, and c be three real numbers satifying `[(a, b, c)]`
`[(1,9,7),(8,2,7),(7,3,7)]=[(0,0,0)]`
If the point P(a, b, c) with reference to (E) lies on the plane `2x+y+z=1`, then the value of `7a+b+c` is

Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0] If the point P(a,b,c) with reference to (E), lies on the plane 2x+y+z=1 , the the value of 7a+b+c is (A) 0 (B) 12 (C) 7 (D) 6

Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0] Let omega be a solution of x^3-1=0 with Im(omega)gt0. I fa=2 with b nd c satisfying (E) then the vlaue of 3/omega^a+1/omega^b+3/omega^c is equa to (A) -2 (B) 2 (C) 3 (D) -3

Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0] Let b=6, with a and c satisfying (E). If alpha and beta are the roots of the quadratic equation ax^2+bx+c=0 then sum_(n=0)^oo (1/alpha+1/beta)^n is (A) 6 (B) 7 (C) 6/7 (D) oo

Let P(a, b, c) be any on the plane 3x+2y+z=7 , then find the least value of 2(a^2+b^2+c^2) .

Let a, b and c be three real numbers satisfying [a" "b" "c"][{:(1,9,7),(8,2,7),(7,9,7):}]=[0"" "0""" "0] and alpha and beta be the roots of the equation ax^(2) + bx + c = 0 , then sum_(n=0)^(oo) ((1)/(alpha)+(1)/(beta))^(n) , is

Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0 . If a=2 with b and c satisfying [abc][{:(1,9,7),(2,8,7),(7,3,7):}]=[0,0,0] , then the value of 3/omega^(a) + 1/omega^(b) + 1/omega^( c) is equal to

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

Show that the points A (1,2), B(-1, -16) and C (0, -7) lie on the graph of the linear equation y=9x -7.

Let a, b and c be real numbers such that a - 7b + 8c = 4 and 8a + 4b - c = 7. What is the value of a^(2) - b^(2) + c^(2) .