Understanding Vector Decomposition

The video tutorial explains vector decomposition, focusing on breaking down a vector into orthogonal components. It introduces the concept of vector projection, providing a formula to calculate the projection of one vector onto another. Through a detailed example, the tutorial demonstrates how to decompose a vector into two orthogonal vectors, verifying their orthogonality using the dot product. The tutorial concludes by summarizing the process and reinforcing the understanding of vector decomposition and orthogonality.

What is another term for vector decomposition?

• Vector subtraction

• Vector multiplication

• Vector composition

• Vector addition

What does it mean for two vectors to be orthogonal?

• They are opposite

• They are perpendicular

• They are equal

• They are parallel

What is the formula for the projection of vector U onto vector V?

• Difference of U and V

• Cross product of U and V

• Dot product of U and V divided by the magnitude of V squared

• Sum of U and V

In the analogy, what does the closed road represent?

• The vector U

• The original path

• The vector V

• The final destination

What is the significance of the 90-degree turn in the analogy?

• It represents the start of the journey

• It represents the end of the journey

• It represents the perpendicular component

• It represents the parallel component

How is the first vector component, W1, calculated?

• By subtracting V from U

• By adding U and V

• By projecting U onto V

• By multiplying U and V

What is the purpose of finding W2 in vector decomposition?

• To find the perpendicular component

• To find the parallel component

• To find the direction

• To find the magnitude

What does the decomposition of vector U into W1 and W2 achieve?

• It divides the vector into parallel and perpendicular components

• It increases the vector's magnitude

• It changes the vector's direction

• It simplifies the vector

What is the result of the dot product of two orthogonal vectors?

• Infinity

• Negative one

• Zero

• One

How can you verify that two vectors are orthogonal?

• By checking if their sum is zero

• By checking if their dot product is zero

• By checking if their cross product is zero

• By checking if their difference is zero