Vectors

Here, you will learn state polygon law of vector addition, subtraction of vectors and multiplication of vector by scalars. Let’s begin – Polygon law of vector Addition (Addition of more than two vectors) Addition of more than two vectors is found to be by repetition of triangle law. Suppose we have to find the sum […]

Here, you will learn triangle law of addition of vectors and parallelogram law of addition of vectors and properties of vector addition. Let’s begin – Addition of Vectors  The vectors have magnitude as well as direction, therefore their addition is different than addition of real numbers. Let \(\vec{a}\) and \(\vec{b}\) be two vectors in a

Here, you will learn vector quantities and scalar quantities and mathematical description of vector and scalar. Let’s begin – Vectors constitute one of the several Mathematical systems which can be usefully employed to provide mathematical handling for certain types of problems in Geometry, Mechanics and other branches of Applied Mathematics. Vectors facilitate mathematical study of

Here, you will learn what is vector triple product formula and linear independence and dependence of vectors. Let’s begin – Vector Triple Product Formula Let \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) be any three vectors, then the expression \(\vec{a}\times (\vec{b}\times\vec{c})\) is a vector & is called a vector triple product. Linear Independence And Dependence of Vectors (a) 

Let \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) be three vectors. Then the scalar \((\vec{a}\times \vec{b}).\vec{c}\) is called the scalar triple product of \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) and is denoted by [\(\vec{a}\) \(\vec{b}\) \(\vec{c}\)]. Thus, we have  [\(\vec{a}\) \(\vec{b}\) \(\vec{c}\)] = \((\vec{a}\times \vec{b}).\vec{c}\) For three vectors \(\vec{a}\), \(\vec{b}\) & \(\vec{c}\), it is also defined as : (\(\vec{a}\times\vec{b}\)).\(\vec{c}\) = \(|\vec{a}||\vec{b}||\vec{c}|sin\theta

Let \(\vec{a}\) and \(\vec{b}\) be two non-zero vectors inclined at an angle \(\theta\). Then the scalar product or dot product of two vectors, \(\vec{a}\) with \(\vec{b}\) is denoted by \(\vec{a}\).\(\vec{b}\) and is defined as, \(\vec{a}\).\(\vec{b}\) = \(|\vec{a}||\vec{b}|cos\theta\)  If \(\vec{a}\) = \(a_1\hat{i}+a_2\hat{j}+a_3\hat{k}\) and \(\vec{b}\) = \(b_1\hat{i}+b_2\hat{j}+b_3\hat{k}\). Then \(\vec{a}\).\(\vec{b}\) = \(a_1b_1+a_2b_2+c_1c_2\) Properties of Dot Product of Two

Cross Product of Vectors Formula : Let \(\vec{a}\) & \(\vec{b}\) are two vectors & \(\theta\) is the angle between them, then cross product of vectors formula is, \(\vec{a}\) \(\times\) \(\vec{b}\) = |\(\vec{a}\)||\(\vec{b}\)|sin\(\theta\)\(\hat{n}\) where \(\hat{n}\) is the unit vector perpendicular to both \(\vec{a}\) & \(\vec{b}\). Properties of Vector Cross Product : (i) \(\vec{a}\) \(\times\) \(\vec{b}\) =

Here you will learn what is unit vector, representation of unit vector, formula for unit vector and how to find the unit vector with examples. Let’s begin – What is a Vector ? A quantity that has both magnitude & direction is called a vector. A vector that has magnitude of 1 is called a