Question Video: Identifying the Features of a 2-Dimensional Vector | Nagwa Question Video: Identifying the Features of a 2-Dimensional Vector | Nagwa

# Question Video: Identifying the Features of a 2-Dimensional Vector Mathematics • First Year of Secondary School

## Join Nagwa Classes

Attend live Mathematics sessions on Nagwa Classes to learn more about this topic from an expert teacher!

Consider the vector in the given diagram. What are the coordinates of its terminal point? What are the coordinates of its initial point? What are the components of the vector?

01:50

### Video Transcript

Consider the vector in the given diagram. What are the coordinates of its terminal point? What are the coordinates of its initial point? What are the components of the vector?

We say that a vector has an initial point, that’s where it starts, and a terminal point, that’s where it ends. So to find the coordinates of the terminal point of the vector in our diagram, that’s the vector 𝐯, we need to find the point at which the line segment that represents that vector ends. Remember, the arrow represents the direction of the vector. So in this case, we move from left to right. This means the vector ends here. We can therefore say its terminal point has coordinates at two, one.

Next, we’re looking to find the coordinates of its initial point. And remember, we said that that’s the start of the line segment. That’s here. The coordinates of this point are negative one, three. So that’s the coordinates of the initial point of our vector.

The third and final part of this question asks us to find the components of the vector. We split two-dimensional vectors into components that represent the horizontal and vertical motion separately. In order to see what these are, we’re going to add a right-angled triangle onto our vector 𝐯. This will split it into its horizontal and vertical components. The right-angled triangle we add is as shown.

Let’s look at the motion in the horizontal direction. We start at 𝑥 equals negative one, and we move one, two, three spaces to the right. Next, we consider the vertical motion. We start at a 𝑦-coordinate of three, and we move one, two units down. We can therefore write the vector 𝐯 as shown. We can use a column or these angled brackets. And the vector is three, negative two.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy