Let a, b and c be three real numbers satisfying
$[\begin{array}{lll} a b c \end{array}] [\begin{array}{lll} 1 9 7 \\ 8 2 7 \\ 7 3 7 \end{array}] = [\begin{array}{lll} 0 0 0 \end{array}]$ (1)
If the point $P (a, b, c)$ with reference to (1), 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

$[\begin{array}{lll} a b c \end{array}] [\begin{array}{lll} 1 9 7 \\ 8 2 7 \\ 7 3 7 \end{array}] = [\begin{array}{lll} 0 0 0 \end{array}]$ (1)

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

Infinity Learn · Accepted Answer

We have $$a+8b+7c=0$$, $$9a+2b+3c=0$$, $$7a+7b+7c=0Subtracting$$ the last equation from first and multiplying thelast equation by (9/7) and subtracting from the second equationwe obtain −$$6a+b=0$$,$$7b+6c=0$$⇒ $$a1=b6=c$$−$$7=k$$ (say)Thus$$, $$a=k$$,$$b=6k$$,$$c=$$−$$7k$$.As $$(a$$,b,$$c)=(k$$,$$6k$$,−$$7k) lies on $$2x+y+z=1$$, we get $$k=1$$.Thus,  $$7a+b+c=7k+6k$$−$$7k=6k=6$$

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Let a, b and c be three real numbers satisfyinga b c1 9 78 2 77 3 7=0 0 0 (1)If the point P(a,b,c) with reference to (1), lies on the plane 2x + y + z = 1, then the value of 7a+b+c is

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