Summary of Calculus 3 - Intro To Vectors

00:00:00 - 00:55:00

This video provides an introduction to vectors, explaining their magnitude and angle, as well as their component form. The video ends with a practice problem, asking the viewer to find the x and y components of a vector with an initial point and terminal point.

• 00:00:00 In this video, we will discuss vectors and their important distinctions from scalar quantities. We will also look at examples of vectors that include magnitude and direction. Finally, we will explore the concept of volume as a scalar or vector quantity.
• 00:05:00 This video provides an introduction to vectors, explaining their magnitude and angle, as well as their component form. The video ends with a practice problem, asking the viewer to find the x and y components of a vector with an initial point and terminal point.
• 00:10:00 Vector algebra is used to find the components of a vector. The magnitude and direction of a vector are determined by its components.
• 00:15:00 This video explains the concept of vectors, and how to calculate the magnitude and direction of vectors. The video also provides an example of how to determine if two vectors are equivalent.
• 00:20:00 In this video, the author explains the concept of vectors, their components, and how to add them together. Two vectors are equivalent if they have the same magnitude and the same slope, but can be different if their components are different. When adding vectors, be sure to connect them from head to tail.
• 00:25:00 This video introduces vector operations, including how to add and subtract vectors, and how to calculate the values of scalar products and sums of vector components.
• 00:30:00 In this video, the author reviews the concept of position vectors and unit vectors. A position vector is any vector that has its initial point placed at the origin, and a unit vector is a vector with a magnitude of one. To find unit vectors, one need to take the vector and divide it by its magnitude.
• 00:35:00 In this video, the author explains how to find a unit vector, and how to represent a vector in its component form. The author also explains how to apply standard unit vectors to vectors in 2 and 3 dimensions.
• 00:40:00 In this video, the standard unit vectors are introduced, and vector operations are explained using them. The unit circle is introduced, and it is explained that its radius is the unit vector. It is shown that vector v can be written as a linear combination of the unit vectors i and j, given that v has a magnitude of 16 and an angle of 30 degrees with the positive x-axis.
• 00:45:00 This video introduces vectors and shows how to find the magnitude and angle of a vector. The video also explains how to find the reference angle using the tangent function.
• 00:50:00 This video provides an introduction to vectors, explaining that the resultant force of two vectors is located in quadrant four. The magnitude of the resulting force and its angle are then determined.
• 00:55:00 In this video, calculus tutor Andrew demonstrates how to calculate the magnitude and angle of a resultant force vector in a problem. The resultant force vector is in quadrant four, which means the angle is 296.6 degrees.