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