Find the vector equation of the plane passing through a point having p

1.	Find the vector equation of the plane passing through a point having position vector \(3\hat i + 2\hat j +\hat k\) and perpendicular to the vector \(4\hat i + 3\hat j +2\hat k\)
Answer» Let \(\overline {a}\) = \(3\hat i + 2\hat j +\hat k\) , \(\overline {n}\) \(4\hat i + 3\hat j +2\hat k\) Vector equation of the plane passing through the point A (\(\overline {a}\)) and perpendicular to the vector \(\overline {n}\) is \(\overline {r} .\overline{n}=\overline {a}.\overline{n}\) ∴ \(\overline {r}\) . (\(4\hat i + 3\hat j +2\hat k\)) = (\(3\hat i + 2\hat j +\hat k\)) . (\(4\hat i + 3\hat j +2\hat k\)) = 3(4) - 2(3) + 1(2) = 12 - 6 + 2 ∴ \(\overline {r}\) . (\(4\hat i + 3\hat j +2\hat k\)) = 8, which is the vector equation of the plane

Find the vector equation of the plane passing through a point having position vector \(3\hat i + 2\hat j +\hat k\) and perpendicular to the vector \(4\hat i + 3\hat j +2\hat k\)

Answer»

Let \(\overline {a}\) = \(3\hat i + 2\hat j +\hat k\) , \(\overline {n}\) \(4\hat i + 3\hat j +2\hat k\)

Vector equation of the plane passing through the point A (\(\overline {a}\)) and perpendicular to the

vector \(\overline {n}\) is \(\overline {r} .\overline{n}=\overline {a}.\overline{n}\)

∴ \(\overline {r}\) . (\(4\hat i + 3\hat j +2\hat k\)) = (\(3\hat i + 2\hat j +\hat k\)) . (\(4\hat i + 3\hat j +2\hat k\))

= 3(4) - 2(3) + 1(2)

= 12 - 6 + 2

∴ \(\overline {r}\) . (\(4\hat i + 3\hat j +2\hat k\)) = 8,

which is the vector equation of the plane

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