Here you will learn law of total probability theorem with examples. Let’s begin – Total Probability Theorem (Law of Total Probability) Let an event A of an experiment occurs with its n mutually exclusive and exhaustive events \(B_1,B_2,B_3….B_n\) then total probability of occurrence of event A is P(A) = \(P(AB_1)\) + \(P(AB_2)\) +……..+ \(P(AB_n)\) P(A) …
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Here you will learn formula for multiplication theorem probability with examples. Let’s begin – Multiplication Theorem Probability It is called compound probability or multiplication theorem. It says the probability that both A and B occur is equal to the probability that A occur times the probability that B occurs given that A has occurred. If …
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 …
Here you learn formula for angle between two lines in 3d in both vector form and cartesian form with examples. Let’s begin – Angle Between Two Lines in 3d (a) Vector Form Let the vector equations of the two lines be \(\vec{r}\) = \(\vec{a_1}\) + \(\lambda \vec{b_1}\) and \(\vec{r}\) = \(\vec{a_2}\) + \(\mu \vec{b_2}\). These …
Here you will learn reduction of cartesian form of line to vector form and vice-versa with examples. Let’s begin – Reduction of Cartesian Form of Line to Vector Form Let the cartesian equations of a line be \(x – x_1\over a\) = \(y – y_1\over b\) = \(z – z_1\over c\) …
Reduction of Cartesian Form of Line to Vector Form and Vice-Versa Read More »
