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Write the perpendicular distance of the plane \( \overrightarrow r.(2\hat i - \hat j + 2\hat k)=12\) from the origin.

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  • The equation of the form $lx+my+nz=d$ where $l,m,n$ are the direction cosines of the normal to the plane,and $d$ is the distance of the normal from the origin.
Step 1:
$\overrightarrow r.(2\hat i-\hat j+2\hat k)=12$
Equation of the given plane is $2x-y+2z=12$--------(1)
Direction ratios of the normal to the plane are $(2,-1,2)$
The direction cosines are
$\Rightarrow \large\frac{2}{3},\frac{-1}{3},\frac{2}{3}$
Step 2:
Divide the equation (1) by 3 we get,
which is of the form $lx+my+nz=d$
Hence the distance of the plane from the origin is 4units.
answered Nov 7, 2013 by sreemathi.v

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