Vectors

Image of a Point in a Plane – Formula and Example

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 …

Equation of Plane Containing Two Lines

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,   [$$\vec{r}$$ $$\vec{b_1}$$ $$\vec{b_2}$$] = [$$\vec{a_2}$$ …

Intersection of a Line and a Plane

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 + …

Angle Between a Line and a Plane

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 …

Distance Between Parallel Planes

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 …

Equation of Plane Parallel to Plane

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 …

Angle Between Two Planes Formula

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 $$cos\theta$$ …

Equation of Plane in Normal Form

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 …