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`
`7a + 7b +7c=0`
Solving these equations, we get
`b=6a`
`rArr c= -7a`
Now, `2x + y + z = 0`
`rArr 2a + 6 a + (-7a) = 1`
`rArr a= 1, b = 6, c=-7`
`therefore 7a + b+ c= + 6 - = 6`