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

Question

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 (A) 0 (B) 12 (C) 7 (D) 6

Tardigrade Admin · Accepted Answer

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

Q. Let $a, b$ and $c$ be three real numbers satisfying
$[a b c] ⎣ ⎡ 187923777 ⎦ ⎤ = [000] (E)$
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

0

12

7

6

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

Q. Let a,b and c be three real numbers satisfying [a​b​c​]⎣⎡​187​923​777​⎦⎤​=[0​0​0​](E) If the point P(a,b,c), with reference to (E), lies on the plane 2x+y+z=1, then the value of 7a+b+c is

0

12

7

6

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

Q. Let $a, b$ and $c$ be three real numbers satisfying
$[a b c] ⎣ ⎡ 187923777 ⎦ ⎤ = [000] (E)$
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

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