Question

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

• A. 0
• B. 12
• C. 7
• D. 6

Answer 1

The correct option is D 6

Given

$a+8b+7c=0$

$9a+2b+3c=0$

$a+b+c=0$

Here $\left[\begin{array}{ccc}1& 8& 7\\ 9& 2& 3\\ 1& 1& 1\end{array}\right]=0$

$\therefore$ The system as infinite many solution

Solving these, we get

$b=6a,c=-7a$

Now, $(a,b,c)$ lies on $2x+y+z=1$

$\therefore 2a+6a-7a=1$

Hence $a=1$

$\therefore 7a+b+c=7+6-7=6$