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  • Let the system of linear equations <img alt="\begin{aligned} & -x+2 y-9 z=7 \\ & -x+3 y+7 z=9 \\ & -2 x+y+5 z=8 \\ & -3 x+y+13 z=7 \end{aligned}" src="https://entrancecorner.

Let the system of linear equations
\begin{aligned} & -x+2 y-9 z=7 \\ & -x+3 y+7 z=9 \\ & -2 x+y+5 z=8 \\ & -3 x+y+13 z=7 \end{aligned}
has a unique solution x=\alpha, y=\beta, z=\gamma Then the distance of the point (\alpha, \beta, \gamma) from the plane 2 x-2 y+z=\lambda. is

Option: 1

7


Option: 2

9


Option: 3

13


Option: 4

11


Answers (1)

best_answer

\begin{aligned} & -x+2 y-9 z=7-(1) \\ & -x+3 y-7 z=9-(2) \\ & -2 x+y+5 z=8-(3) \\ & (2)-(1) \\ & y+16 z=2(4) \\ & (3)-2 x(1) \\ & -3 y+23 z=-6-(5) \\ & 3 x(4)+(5) \\ & 71 z=0 \Rightarrow z=0 \\ & y=2 \\ & x=-3 \\ & (-3,2,0)-(a, \beta, \gamma) \\ & \text { Put in }-3 x+y+13 z=1 \\ & \lambda=9+2=11 \\ & d=|-6-4-11|=? \\ & 3 \end{aligned}

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Pankaj Sanodiya

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