Question

Let $a,b\text{and}c$ be three real numbers satisfying
$\left[\begin{array}{ccc}a& b& c\end{array}\right]\left[\begin{array}{ccc}1& 9& 7\\ 8& 2& 7\\ 7& 3& 7\end{array}\right]=\left[\begin{array}{ccc}0& 0& 0\end{array}\right]$ . . . (i)


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

• A. \N
• B. 12
• C. 7
• D. 6

Answer 1

The correct option is D 6

On multiplying matrices, we have
$\left[\begin{array}{ccc}a+8b+7c& 9a+2b+3c& 7a+7b+7c\end{array}\right]=\left[\begin{array}{ccc}0& 0& 0\end{array}\right]$
On solving the 3 equations, we get $b=6a\text{and}c=-7a$

As P(a, b, c) lies on 2x + y + z = 1 $\Rightarrow$ 2a + b + c = 1
$\Rightarrow$ 2a + 6a - 7a = 1
$\Rightarrow$ a = 1, b = 6, c =-7
$\therefore$ 7a + b + c = 7 + 6 - 7 = 6