Introduction to Vectors

This course serves as an introduction to the topic of vectors. The first section covers some basic concepts about 2D vectors, position vectors, direction cosines. It also explains different types of vectors, namely, zero, unit, collinear, equal, coinitial vectors. The next section covers how to find the magnitude of a vector and how to perform the addition and multiplication of vectors. It also explains the concepts of dot product and cross product and how to find them.

15 topics

337 lectures

Educators

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Course Curriculum

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Introduction to Vectors Lectures

Introduction to Vectors

2D Vector Basics - Overview

In mathematics, a vector (from the Latin vehere "to transport") is a geometric object that has a magnitude (or length) and a direction. Vectors can be added to other vectors according to vector algebra, and can be multiplied by a scalar (real number). A vector is what is called a "linear" quantity; its magnitude is independent of the chosen basis, and is determined by the component vectors' components. A vector can be pictured as an arrow (or a directed line segment) with a definite magnitude and direction, and having a definite position relative to a chosen origin. The magnitude of the vector is the length of the arrow. The direction of a vector is the direction of the arrow.

Lily An

Introduction to Vectors

2D Vector Basics - Example 1

In mathematics, a vector (from the Latin vehere "to transport") is a geometric object that has a magnitude (or length) and a direction. Vectors can be added to other vectors according to vector algebra, and can be multiplied by a scalar (real number). A vector is what is called a "linear" quantity; its magnitude is independent of the chosen basis, and is determined by the component vectors' components. A vector can be pictured as an arrow (or a directed line segment) with a definite magnitude and direction, and having a definite position relative to a chosen origin. The magnitude of the vector is the length of the arrow. The direction of a vector is the direction of the arrow.

Lily An

Introduction to Vectors

2D Vector Basics - Example 2

In mathematics, a vector (from the Latin vehere "to transport") is a geometric object that has a magnitude (or length) and a direction. Vectors can be added to other vectors according to vector algebra, and can be multiplied by a scalar (real number). A vector is what is called a "linear" quantity; its magnitude is independent of the chosen basis, and is determined by the component vectors' components. A vector can be pictured as an arrow (or a directed line segment) with a definite magnitude and direction, and having a definite position relative to a chosen origin. The magnitude of the vector is the length of the arrow. The direction of a vector is the direction of the arrow.

Lily An

Introduction to Vectors

2D Vector Basics - Example 3

In mathematics, a vector (from the Latin vehere "to transport") is a geometric object that has a magnitude (or length) and a direction. Vectors can be added to other vectors according to vector algebra, and can be multiplied by a scalar (real number). A vector is what is called a "linear" quantity; its magnitude is independent of the chosen basis, and is determined by the component vectors' components. A vector can be pictured as an arrow (or a directed line segment) with a definite magnitude and direction, and having a definite position relative to a chosen origin. The magnitude of the vector is the length of the arrow. The direction of a vector is the direction of the arrow.

Lily An

Introduction to Vectors

2D Vector Basics - Example 4

In mathematics, a vector (from the Latin vehere "to transport") is a geometric object that has a magnitude (or length) and a direction. Vectors can be added to other vectors according to vector algebra, and can be multiplied by a scalar (real number). A vector is what is called a "linear" quantity; its magnitude is independent of the chosen basis, and is determined by the component vectors' components. A vector can be pictured as an arrow (or a directed line segment) with a definite magnitude and direction, and having a definite position relative to a chosen origin. The magnitude of the vector is the length of the arrow. The direction of a vector is the direction of the arrow.

Lily An

Introduction to Vectors

2D Vector Operations - Overview

In mathematics, a vector (from the Latin "vehere", "to carry") is a geometric object that has a magnitude (or length) and a direction. A vector can be thought of as an arrow in Euclidean space, drawn from an initial point A to a terminal point B, called the vector's tail (or head). A vector is what is needed to "carry" the point B to the point A. Vectors also include the notion of a vector space, which is an abstract collection of vectors that can be added together and multiplied by numbers, using the operations of vector addition and scalar multiplication. In mathematics, a vector is what is needed to "carry" the point B to the point A. Vectors also include the notion of a vector space, which is an abstract collection of vectors that can be added together and multiplied by numbers, using the operations of vector addition and scalar multiplication.

Lily An

Introduction to Vectors

2D Vector Operations - Example 1

In mathematics, a vector (from the Latin "vehere", "to carry") is a geometric object that has a magnitude (or length) and a direction. A vector can be thought of as an arrow in Euclidean space, drawn from an initial point A to a terminal point B, called the vector's tail (or head). A vector is what is needed to "carry" the point B to the point A. Vectors also include the notion of a vector space, which is an abstract collection of vectors that can be added together and multiplied by numbers, using the operations of vector addition and scalar multiplication. In mathematics, a vector is what is needed to "carry" the point B to the point A. Vectors also include the notion of a vector space, which is an abstract collection of vectors that can be added together and multiplied by numbers, using the operations of vector addition and scalar multiplication.

Lily An

Introduction to Vectors

2D Vector Operations - Example 2

In mathematics, a vector (from the Latin "vehere", "to carry") is a geometric object that has a magnitude (or length) and a direction. A vector can be thought of as an arrow in Euclidean space, drawn from an initial point A to a terminal point B, called the vector's tail (or head). A vector is what is needed to "carry" the point B to the point A. Vectors also include the notion of a vector space, which is an abstract collection of vectors that can be added together and multiplied by numbers, using the operations of vector addition and scalar multiplication. In mathematics, a vector is what is needed to "carry" the point B to the point A. Vectors also include the notion of a vector space, which is an abstract collection of vectors that can be added together and multiplied by numbers, using the operations of vector addition and scalar multiplication.

Lily An

Introduction to Vectors

2D Vector Operations - Example 3

In mathematics, a vector (from the Latin "vehere", "to carry") is a geometric object that has a magnitude (or length) and a direction. A vector can be thought of as an arrow in Euclidean space, drawn from an initial point A to a terminal point B, called the vector's tail (or head). A vector is what is needed to "carry" the point B to the point A. Vectors also include the notion of a vector space, which is an abstract collection of vectors that can be added together and multiplied by numbers, using the operations of vector addition and scalar multiplication. In mathematics, a vector is what is needed to "carry" the point B to the point A. Vectors also include the notion of a vector space, which is an abstract collection of vectors that can be added together and multiplied by numbers, using the operations of vector addition and scalar multiplication.

Lily An

Introduction to Vectors

2D Vector Operations - Example 4

In mathematics, a vector (from the Latin "vehere", "to carry") is a geometric object that has a magnitude (or length) and a direction. A vector can be thought of as an arrow in Euclidean space, drawn from an initial point A to a terminal point B, called the vector's tail (or head). A vector is what is needed to "carry" the point B to the point A. Vectors also include the notion of a vector space, which is an abstract collection of vectors that can be added together and multiplied by numbers, using the operations of vector addition and scalar multiplication. In mathematics, a vector is what is needed to "carry" the point B to the point A. Vectors also include the notion of a vector space, which is an abstract collection of vectors that can be added together and multiplied by numbers, using the operations of vector addition and scalar multiplication.

Lily An

Introduction to Vectors

Dot Product - Overview

In mathematics, the dot product or scalar product is a binary operation on two vectors in three-dimensional space. It is defined as the product of the magnitudes of the two vectors and the cosine of the angle between them. The dot product is a special case of the cross product, and is equivalent to the cross product for vectors that are perpendicular to each other. The dot product is denoted by a dot placed between the two vectors.

Lily An

Introduction to Vectors

Dot Product - Example 1

In mathematics, the dot product or scalar product is a binary operation on two vectors in three-dimensional space. It is defined as the product of the magnitudes of the two vectors and the cosine of the angle between them. The dot product is a special case of the cross product, and is equivalent to the cross product for vectors that are perpendicular to each other. The dot product is denoted by a dot placed between the two vectors.

Lily An

Introduction to Vectors

Dot Product - Example 2

In mathematics, the dot product or scalar product is a binary operation on two vectors in three-dimensional space. It is defined as the product of the magnitudes of the two vectors and the cosine of the angle between them. The dot product is a special case of the cross product, and is equivalent to the cross product for vectors that are perpendicular to each other. The dot product is denoted by a dot placed between the two vectors.

Lily An

Introduction to Vectors

Dot Product - Example 3

In mathematics, the dot product or scalar product is a binary operation on two vectors in three-dimensional space. It is defined as the product of the magnitudes of the two vectors and the cosine of the angle between them. The dot product is a special case of the cross product, and is equivalent to the cross product for vectors that are perpendicular to each other. The dot product is denoted by a dot placed between the two vectors.

Lily An

Introduction to Vectors

Dot Product - Example 4

In mathematics, the dot product or scalar product is a binary operation on two vectors in three-dimensional space. It is defined as the product of the magnitudes of the two vectors and the cosine of the angle between them. The dot product is a special case of the cross product, and is equivalent to the cross product for vectors that are perpendicular to each other. The dot product is denoted by a dot placed between the two vectors.

Lily An