Question

Let a, b, c be three real numbers satisfying

[a b c][(1,9,7),(8,2,7),(7,3,7)] = [0 0 0] ... (E).

If the point P(a, b, c), with reference to (E), lies on the plane 2x + y + z = 1, the value of 7a + b + c is

(a) 0

(b) 12

(c) 7

(d) 6

Answer 1

Answer is (d) 6 

Given 

a + 8b + 7c = 0

9a + 2b + 3c = 0

and a + b + c = 0

Solving, we get b = 6a, c = – 7a

Since the point P lies on the plane, so

2a + b + c = 1 

2a + 6a – 7a = 1 

a = 1

Thus, b = 6 and c = –7

Now the value of 7a + b + c

= 7 + 6 – 7

= 6