Complex Vectors and Their Properties

This video tutorial explains how to add complex vectors, which are not limited to horizontal or vertical directions. It covers finding x and y components of vectors, calculating the resultant vector using the Pythagorean theorem, and determining the angle using the tangent inverse. The tutorial includes examples to illustrate the process and emphasizes the importance of practice in mastering vector addition.

What is a complex vector?

• A vector that only points downwards

• A vector that only points upwards

• A vector that can have any angle

• A vector that is always horizontal or vertical

What is the first step in adding complex vectors?

• Find the resultant vector directly

• Use the Pythagorean theorem

• Find the x and y components of each vector

• Connect vectors tip-to-tail

How do you calculate the magnitude of the resultant vector?

• By using the Pythagorean theorem on the x and y components

• By multiplying the x and y components

• By subtracting the x component from the y component

• By adding the x and y components

What is the formula to find the angle of the resultant vector?

• tan inverse of the sum of x components over the sum of y components

• tan inverse of the sum of y components over the sum of x components

• sin inverse of the sum of x components over the sum of y components

• cos inverse of the sum of y components over the sum of x components

In the first example, what is the x component of vector A?

• 4.7

• -8.7

• 5

• 0

What is the angle of the resultant vector in the first example?

• 44 degrees

• 90 degrees

• 67 degrees

• 30 degrees

In the second example, what is the y component of vector A?

• 10

• -10

• 0

• 7.5

Which quadrant is the resultant vector in the second example located?

• Third quadrant

• Second quadrant

• First quadrant

• Fourth quadrant

What is the magnitude of the resultant vector in the second example?

• 7.3

• 10.5

• 44

• 67

Why is it important to note the direction of vectors?

• Because vectors can only point downwards

• Because vectors can only point upwards

• To determine if vectors are positive or negative

• To ensure vectors are always horizontal