InstructorPriyanka Pandey
TypeOnline Course
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A vector refers to any quantity that needs a magnitude and a direction in order to fully describe the quantity. In this lesson you will learn about the properties of vectors (magnitude and direction) and how to determine what quantities are vectors and what are not vectors.

Definition of a Vector Quantity

When someone tells you to throw a ball twice as hard and to the left, a vector was just used. When someone tells you to drive northeast for about five miles, a vector was just used. So what exactly is a vector? Any quantity that needs to be fully described by identifying its magnitude and direction is referred to as a vector quantity. By magnitude, we mean size of the quantity, such as length or strength. By direction, we mean where the vector is pointing or where it is being directed, such as left or right, north, south, east, or west, or even up or down.

How a Vector Is Represented

When a vector is drawn, it is represented by an arrow whose length represents the vector’s magnitude and whose arrow head points in the direction of the vector as shown in the figure below.

If the vector represents a quantity in one dimension–x-direction (left and right) or y-direction (up and down)–then a vector will be written as a number with a plus (+) or minus (-) sign in front of it. The plus refers to pointing right or up, and the minus refers to pointing left or down. In two dimensions (x and y), a vector will be represented with a number for magnitude and an angle for direction.

Section 1Introduction To Vectors
Section 2Introduction To Types Of Vectors
Section 3Addition Of Vectors
Lecture 3Addition Of Vectors
Lecture 4Addition Of Vectors Theorem - 1
Lecture 5Addition Of Vectors Example – 1
Section 4Introduction To Scalar Multiplication Of A Vector
Section 5Introduction To The Vector Equation Of A Plane
Section 6Introduction To Vector Equation Of A Line And A Plane
Section 7Introduction To Scalar Triple Product
Section 8Introduction To The Vector Triple Product
Section 9Introduction To Dot Product
Lecture 11Introduction To Dot Product
Lecture 12Theorem On Dot Product
Lecture 13Dot Product Example – 1
Section 10Introduction To Cross Product Part
Lecture 14Introduction To Cross Product Part - 1
Lecture 15Introduction To Cross Product Part - 2
Lecture 16 Cross Product Example – 1
Section 11 Introduction To Coplanar Vectors
Section 12 Introduction To Collinear Vectors
Lecture 18 Introduction To Collinear Vectors
Lecture 19 Collinear Vectors Example – 1
Section 13 Introduction To Direction Ratios And Direction Cosines
Section 14 Introduction To Orthogonal Projection
Section 15Angle Between Two Vectors
Lecture 22Angle Between Two Vectors
Lecture 23 Angle Between Two Non-Zero
Section 16 How To Find Area Of The Triangle Using Vector Methods
Section 17 How To Find Area Of The Parallelogram Using Vector Methods
Section 18 How To Find The Volume Of A Parallelepiped
Section 19 How To Find The Volume Of A Tetrahedron