Here you will learn how to find image of a point in a plane formula with examples. Let’s begin – Image of a Point in a Plane Let P and Q be two points and let \(\pi\) be a plane such that (i) line PQ is perpendicular to the plane \(\pi\) and, (ii) mid-point of …
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Here you will learn how to find equation of plane containing two lines with examples. Let’s begin – Equation of Plane Containing Two Lines (a) Vector Form If the lines \(\vec{r}\) = \(a_1 + \lambda\vec{b_1}\) and \(\vec{r}\) = \(a_2 + \mu\vec{b_2}\) are coplanar, then \(\vec{r_1}\).(\(\vec{b_1}\times \vec{b_2}\)) = \(\vec{a_2}\).(\(\vec{b_1}\times \vec{b_2}\)) or, [\(\vec{r}\) \(\vec{b_1}\) \(\vec{b_2}\)] = [\(\vec{a_2}\) …
Here you will learn how to find intersection of a line and a plane with examples. Let’s begin – Intersection of a Line and a Plane Let the equation of a line be \(x – x_1\over l\) = \(y – y_1\over m\) = \(z – z_1\over n\) and that of a plane be ax + …
Here you will learn formula to find angle between a line and a plane with examples. Let’s begin – Angle Between a Line and a Plane The angle between a line and a plane is the complement of the angle between the line and normal to the plane (a) Vector Form The angle \(\theta\) between …
Here you will learn how to find distance between parallel planes with examples. Let’s begin – Distance Between Parallel Planes Let ax + by + cz + \(d_1\) = 0 and ax + by + cz + \(d_2\) = 0 be two parallel planes. In order to find the distance between them, we may follow …
Here you will learn how to find the distance of a point from a plane formula with examples. Let’s begin – Distance of a Point from a Plane (a) Vector Form The length of the perpendicular from a point having position vector \(\vec{a}\) to the plane \(\vec{r}\).\(\vec{n}\) = d is p = \(|\vec{a}.\vec{n} – d|\over …
Here you will learn what is the equation of plane passing through intersection of two planes with examples. Let’s begin – Equation of Plane Passing Through Intersection of Two Planes (a) Vector Form The equation of a plane passing through the intersection of the planes \(\vec{r}.\vec{n_1}\) = \(d_1\) and \(\vec{r}.\vec{n_2}\) = \(d_2\) is given by …
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Here you will learn equation of plane parallel to plane with examples. Let’s begin – Equation of Plane Parallel to Plane (a) Vector Form Since parallel planes have the common normal, therefore equation of a plane parallel to the plane \(\vec{r}\).\(\vec{n}\) = \(\vec{d_1}\) is \(\vec{r}\).\(\vec{n}\) = \(\vec{d_2}\) where \(\vec{d_2}\) is constant determined by the given …
Here you will learn how to find angle between two planes formula with examples. Let’s begin – Angle Between Two Planes Formula The angle between two planes is defined as the angle between their normals. (a) Vector Form The angle \(\theta\) between the planes \(\vec{r}\).\(\vec{n_1}\) = \(\vec{d_1}\) and \(\vec{r}\).\(\vec{n_2}\) = \(\vec{d_2}\) is given by \(cos\theta\) …
Here you will learn equation of plane in normal form with example. Let’s begin – Equation of Plane in Normal Form (a) Vector Form The vector equation of a plane normal to unit vector \(\hat{n}\) and at a distance d from the origin is \(\vec{r}.\hat{n}\) = d Remark 1 : The vector equation of ON …
