Let $\mathrm{a}, \mathrm{b}$ and c be three real numbers satisfying $\left[\begin{array}{lll}\mathrm{a} & \mathrm{b} & \mathrm{c}\end{array}\right]\left[\begin{array}{lll}1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7\end{array}\right]=\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]$
If the point $\mathrm{P}(\mathrm{a}, \mathrm{b}, \mathrm{c})$, with reference to $(\mathrm{E})$, lies on the plane $2 \mathrm{x}+\mathrm{y}+\mathrm{z}=1$, then the value of $7 \mathrm{a}+\mathrm{b}+\mathrm{c}$ is
Select the correct option:
A
0.0
B
12
C
7
D
6
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$\begin{aligned} & a+8 b+7 c=0 \\ & 9 a+2 b+3 c=0\end{aligned}$ $$
a+b+c=0
$$
Solving these we get
$$
\begin{aligned}
& b=6 a \Rightarrow c=-7 a \\
& \text { now } 2 x+y+z=0 \\
& \Rightarrow 2 a+6 a+(-7 a)=1 \Rightarrow a=1, b=6, c=-7
\end{aligned}
$$
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