Question Video: Using Initial and Terminal Points to Find the Components of a Vector | Nagwa Question Video: Using Initial and Terminal Points to Find the Components of a Vector | Nagwa

# Question Video: Using Initial and Terminal Points to Find the Components of a Vector Mathematics • First Year of Secondary School

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Consider the vector ππ for π΄(3, 2) and π΅(6, 9). Write vector ππ in the form β©π, πβͺ.

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### Video Transcript

Consider the vector ππ for point π΄ with coordinates three, two and π΅ with coordinates six, nine. Write vector ππ in component form π, π.

To find the components π and π of the vector ππ, we consider the horizontal and vertical distances and directions from π΄, which is the initial point, to π΅, which is the terminal point. We see that the horizontal distance is three units moving to the right. So π is positive three. And in fact this is the difference between the two π₯-coordinates of points π and π, that is, six minus three, which is positive three. The vertical distance is seven units up. Thatβs positive seven. And this is the difference between the π¦-coordinates of the two points π΄ and π΅. Hence, we can write the vector from π΄ to π΅ as ππ equals three, seven.

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