1. Tardigrade
  2. Question
  3. Mathematics
  4. Let a, b and 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 2 x + y + z =1, then the value of 7 a + b + c is

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Q. Let $a, b$ and $c$ be three real numbers satisfying
$\begin{bmatrix}a & b & c\end{bmatrix}\begin{bmatrix}1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7\end{bmatrix}=\begin{bmatrix}0 & 0 & 0\end{bmatrix}( E )$
If the point $P ( a , b , c )$, with reference to $( E )$, lies on the plane $2 x + y + z =1$, then the value of $7 a + b + c$ is

JEE AdvancedJEE Advanced 2011

Solution:

$a+8 b+7 c=0$
$9 a+2 b+3 c=0$
$a+ b+ c=0$
Solving these we get
$b =6 a \Rightarrow c =-7 a$
now $2 x + y + z =0$
$\Rightarrow 2 a +6 a +(-7 a)=1$
$\Rightarrow a =1, b =6, c =-7$