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A straight line joining the points (1,1,1) and (0,0,0) intersects the plane $2 x+2 y+z=10$ at
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Verified Answer
The correct answer is:
(2,2,2)
Equation of line joining the points (1,1,1) and (0,0,0) is
$$
\begin{aligned}
\frac{x-0}{1-0} &=\frac{y-0}{1-0}=\frac{z-0}{1-0}=\lambda \\
\Rightarrow & x=y=z=\lambda
\end{aligned}
$$
So, the point is $(\lambda, \lambda, \lambda)$ The point intersects the plane $2 x+2 y+z=10$
$\therefore 2(\lambda)+2(\lambda)+\lambda=10$
$\Rightarrow 5 \lambda=10$
$\Rightarrow \lambda=2$
Hence, the point is (2,2,2) .
$$
\begin{aligned}
\frac{x-0}{1-0} &=\frac{y-0}{1-0}=\frac{z-0}{1-0}=\lambda \\
\Rightarrow & x=y=z=\lambda
\end{aligned}
$$
So, the point is $(\lambda, \lambda, \lambda)$ The point intersects the plane $2 x+2 y+z=10$
$\therefore 2(\lambda)+2(\lambda)+\lambda=10$
$\Rightarrow 5 \lambda=10$
$\Rightarrow \lambda=2$
Hence, the point is (2,2,2) .
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