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प्रश्न
Find the cartesian form of the equation of the plane `bar r=(hati+hatj)+s(hati-hatj+2hatk)+t(hati+2hatj+hatj)`
उत्तर
The equation `barr=bara+sbarb+tbarc` represents a plane passing through a point having position vector a and parallel to the vectors b and c .
Here, `bara=hati+hatj, barb=hati-hatj+2hatk and barc=hati+2hatj+hatk`
The given plane is perpendicular to the vector `barn`
Vector equation of the plane in scalar product form is `barr.barn=bara.barn`
`therefore x(-5)+y(1)+z(3)=-4`
`therefore -5x+y+3z=-4`
`therefore 5x-y-3z=4`
which is the cartesian form of the equation of the plane
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