Calculus III: The Dot Product (Level 4 of 12)

The video tutorial covers advanced examples of the dot product, starting with unit vectors in an equilateral triangle and calculating their dot products. It then applies the dot product to a real-world scenario involving a street vendor's revenue. The tutorial explains how to find vectors perpendicular to a given vector and solve for values that make vectors orthogonal. The video concludes with a preview of the next topic: finding angles between vectors.

What is the dot product of two unit vectors forming a 60-degree angle in an equilateral triangle?

• 1

• 1/2

• -1/2

• 0

What is the angle between vectors u and w in the equilateral triangle problem?

• 180 degrees

• 60 degrees

• 90 degrees

• 120 degrees

In the context of the street vendor problem, what does the dot product of vectors F and P represent?

• The total number of items sold

• The vendor's total revenue for the day

• The average price of items

• The difference in prices of items

In the vendor problem, if the price of burritos changes to $6, what would be the new component of vector P?

• (0.5, 5, 1)

• (0.5, 4, 1)

• (0.5, 7, 1)

• (0.5, 6, 1)

Which of the following is a vector perpendicular to vector v with components (a, b)?

• (b, a)

• (-a, -b)

• (-b, a)

• (a, -b)

What is the value of k that makes vectors A and B perpendicular?

• 4

• 3/2

• 2

• 1

For vectors (-6, b, 2) and (b, b^2, b), which value of b makes them orthogonal?

• 0

• 5

• 1

• 3