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JEE Mains · Maths · STD 12 - 11. three dimension geometry
If \(x\, = a\), \(y\, = b\), \(z\, = c\) is a solution of the system of linear equations \(x+8y+ 7z\,= 0\) ; \(9x+ 2y+ 3z\, = 0\) ; \(x+y+z\, = 0\) such that the point \((a, b, c)\) lies on the plane \(x + 2y + z\, = 6\), then \(2a + b + c\) equals
- A \(-1\)
- B \(0\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
\(x+8 y+7 z =0 \) \(9 x+2 y+3 z =0 \) \(x+y+z =0\) \(x=\lambda \quad|y=6 \lambda| \quad z=-7 \lambda\) \(\begin{array}{*{20}{c}} {\boxed{x = \lambda }}&{\boxed{y = 6\lambda }}&{\boxed{z = - 7\lambda }} \end{array}\)…
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