Vectors

Triangle Law of Addition of Vectors | Parallelogram Law

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

Triangle Law of Addition of Vectors | Parallelogram Law Read More »

Vector Quantities and Scalar Quantities

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

Vector Quantities and Scalar Quantities Read More »

What is Vector Triple Product

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) 

What is Vector Triple Product Read More »

What is Scalar Triple Product – Properties and Examples

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

What is Scalar Triple Product – Properties and Examples Read More »

What is Dot Product of Two Vectors ?

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

What is Dot Product of Two Vectors ? Read More »

Cross Product of Vectors Formula [ Vector Product ]

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) \(\vec{a}\) \(\times\) \(\vec{b}\) =

Cross Product of Vectors Formula [ Vector Product ] Read More »