Here you will learn what is the equation of plane in vector form with examples. Let begin – Equation of Plane in Vector form The vector equation of a plane passing through a point having position vector \(\vec{a}\) and normal to vector \(\vec{n}\) is \((\vec{r} – \vec{a}).\vec{n}\) = 0 or, \(\vec{r}\).\(\vec{n}\) = \(\vec{a}\).\(\vec{n}\). Note 1 …
Here you will learn intercept form of a plane equation with examples. Let’s begin – Intercept Form of a Plane The equation of a plane intercepting lengths a, b and c with x-axis, y-axis and z-axis respectively is \(x\over a\) + \(y\over b\) + \(z\over c\) = 1 Note : 1). The above equation is …
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Here you will learn the equation of plane passing through three points with example. Let’s begin – Equation of a Plane Passing Through a Given Point The general equation of a plane passing through a point \((x_1, y_1, z_1\)) is \(a(x – x_1) + b(y – y_1) + c(z – z_1)\) = 0, where a, …
Here you will learn what is a plane and what is the general equation of a plane. Let’s begin – What is Plane ? A plane is a surface such that if any two points are taken on it, the line segment joining them lies completely on the surface. In other words, every point on …
Here you will learn types of vectors in maths. Let’s begin – Types of Vectors in Maths (a) Zero or Null Vector A vector whose initial and terminal points are coincident is called the zero or the null vector. Thus, the modulus of the null vector is zero but it can be thought of as …
Here you will learn definition of coplanar vectors with example and test of coplanarity of four points. Let’s begin – Coplanar Vectors A system of vectors is said to be coplanar, if their supports are parallel to the same plane. Note : Two vectors are coplanar. Theorem 1 (Test of Coplanarity of Three vectors) Let …
Here you will learn formula to find the distance between two parallel lines in 3d with example. Let’s begin – Distance Between Two Parallel Lines in 3d Let \(l_1\) and \(l_2\) be two parallel lines having vector equations \(l_1\) : \(\vec{r}\) = \(\vec{a_1}\) + \(\lambda\)\(\vec{b}\) and \(l_2\) : \(\vec{r}\) = \(\vec{a_2}\) + \(\mu\)\(\vec{b}\). The shortest …
Here you will learn formula to find the distance between two lines in 3d in both vector form and cartesian form with example. Let’s begin – Distance Between Two Lines in 3d (a) Vector Form Let \(l_1\) and \(l_2\) be two lines having vector equations \(l_1\) : \(\vec{r}\) = \(\vec{a_1}\) + \(\lambda\)\(\vec{b_1}\) and \(l_2\) : \(\vec{r}\) …
Here you will learn how to find perpendicular distance of a point from a line in 3d in both vector form and cartesian form. Let’s begin – Perpendicular Distance of a Point From a Line in 3d (a) Cartesian Form Algorithm : Let P\((\alpha, \beta, \gamma)\) be the given point, and let the given line …
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Here you will learn how to find point of intersection of two lines in 3d for both vector and cartesian form with example. Let’s begin – Point of Intersection of Two lines in 3d (a) Cartesian Form Algorithm : Let the two lines be \(x – x_1\over a_1\) = \(y – y_1\over b_1\) = \(z …
