Matrices and Determinants 1 Question 14

Passage Based Problems

Passage

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} \quad $ …(i)

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

(a) 0

(b) 12

(c) 7

(d) 6

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Answer:

Correct Answer: 14. (d)

Solution:

  1. As $(a, b, c)$ lies on $2 x+y+z=1 \Rightarrow 2 a+b+c=1$

$ \begin{array}{lll} \Rightarrow & 2 a+6 a-7 a =1 \\ \Rightarrow & a =1, b=6, c=-7 \\ \therefore & 7 a+b +c=7+6-7=6 \end{array} $



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