Vectors

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 […]

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

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