SATHEE: Matrices and Determinants 1 Question 14

Matrices and Determinants 1 Question 14

Passage Based Problems

Passage

Let $a$ , $b$ and $c$ be three real numbers satisfying

$[\begin{matrix} a & b & c \end{matrix}]$ $[\begin{matrix} 1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7 \end{matrix}]$ = $[\begin{matrix} 0 & 0 & 0 \end{matrix}]$ …(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

Show Answer

Answer:

Correct Answer: 14. (d)

Solution:

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

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

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Matrices and Determinants 1 Question 14

14. 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

Answer:

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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