Question

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

Answer 1

Correct Answer - D
`a+8b+7c=0`
`9a+2b+3c=0`
`a+b+c=0`
Solving these, we get
`b=6a implies c=-7a`
now `2x+y+z=0`
`implies 2a+6a+(-7a)=1`
`implies a=1, b=6, c=-7`.