Vectors

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 \(x – x_1\over a\) = \(y – y_1\over b\) = \(z – z_1\over c\)         

Here you will learn cartesian equation of line in 3d passing through a fixed point and passing through two points. Let’s begin – Cartesian Equation of a Line The cartesian equations of a straight line passing through a fixed point \((x_1, y_1, z_1)\) having direction ratios proportional to a, b, c is given by \(x

Here you will learn equation of a line in vector form passing through a fixed point and passing through two points. Let’s begin – Equation of a Line in Vector Form The vector equation of a straight line passing through a fixed point with position vector \(\vec{a}\) and parallel to a given vector \(\vec{b}\) is 

Here, we will find the formula for angle between two vectors in terms of their direction cosines and also in terms of their direction ratios. The angle between two lines is defined as the angle between two vectors parallel to them. So, the results derived for vectors will also be applicalble to lines, Let’s begin

In this post you will learn how to find direction cosines and direction ratios of line of the vector with examples. Let’s begin – Direction Cosines and Direction Ratios of Line Direction cosines The direction cosines of a line are defined as the direction cosines of any vector whose support is the given line. It

Here you will learn section formula in 3d for both internal and external division with examples. For distance formula and section formula in 2d for internal and external division see this What is the Section Formula | Distance Formula in 2d. Let’s begin – Section Formula in 3d (a) Internal Division Let P\((x_1, y_1, z_1)\)

Here you will learn distance formula in 3d to calculate distance between two points with example. Let’s begin – Distance Formula in 3d The distance between the points P\((x_1, y_1, z_1)\) and Q\((x_2, y_2, z_2)\) is given by PQ = \(\sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2 + (z_2 – z_1)^2}\) Proof : Let O

Here you will learn some scalar and vector examples for better understanding of scalar and vector concepts. Example 1 : Find the vector of magnitude 5 which are perpendicular to the vectors \(\vec{a}\) = \(2\hat{i} + \hat{j} – 3\hat{k}\) and \(\vec{b}\) = \(\hat{i} – 2\hat{j} + \hat{k}\). Solution : Unit vectors perpendicular to \(\vec{a}\) &

Here, you will learn definition of collinear vectors, coplanar vectors, co-initial vectors and test of collinearity of three points. Let’s begin – Definition of Collinear Vectors Two vectors are said to be collinear if their supports are parallel disregards to their direction. Collinear vectors are also called Parallel vectors. If they have the same direction