Find the cartesian form of the equation of the plane vector r (i+j) + s(i-j+2k)+ t(i+2j+k)

Question

Find the cartesian form of the equation of the plane \(\overline r\) = (\(\hat i+\hat j\)) +s (\(\hat i+\hat j\) +\(2\hat k\)) +t (\(\hat i+2\hat j\) +\(\hat k\))

Answer 1

The equation \(\overline r\) = \(\overline a\) + s\(\overline b\) + t\(\overline c\) represents a plane passing through a point having position vector \(\overline a\) and parallel to the vectors \(\overline b\) and \(\overline c\) .

Here, \(\overline a\) = \(\hat i+\hat j\), \(\overline b\) (\(\hat i+\hat j\) +\(2\hat k\)) and \(\overline c\) (\(\hat i+2\hat j\) +\(\hat k\))

The given plane is perpendicular to the vector \(\overline n\)

Which is the cartesian form of the equation of the plane.