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Question

Let a,b and c be three real numbers satisfying
[abc]⎡⎢⎣197827737⎤⎥⎦=[000] . . . (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
12
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B
7
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C
6
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Solution

The correct option is C 6
On multiplying matrices, we have
[a+8b+7c9a+2b+3c7a+7b+7c]=[000]
On solving the 3 equations, we get b=6a and c=7a

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

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