# Question Video: Finding the Components of a Vector Shown on a Grid Physics

Write π in component form.

02:17

### Video Transcript

Write π in component form.

Now, the first thing to be aware of here is that π marked on the diagram is written in bold, whereas when we handwrite it, we put this little half arrow over the top. These are both just ways of indicating that π is a vector, meaning it has both magnitude and direction. Now, what we mean by writing π in component form is we want to write it in the form π is equal to π sub π₯ π’ hat plus π sub π¦ π£ hat. Here, π’ hat and π£ hat are unit vectors. Since our vector π is drawn on a grid, we can define one grid square to be one unit. And then π’ hat is one unit in the horizontal direction, and π£ hat is one unit in the vertical direction.

Since π’ hat and π£ hat are providing the direction of our vector, we then have π sub π₯ and π sub π¦ to provide the magnitude of the vector, where π sub π₯ is the magnitude in the horizontal direction and π sub π¦ is the magnitude in the vertical direction. So letβs first find π sub π₯. We do this by starting at the tail of vector π, which is at the origin, and then counting horizontally one, two, three, four, five, six until weβre in line with the tip of the vector. That was six grid squares and in the same direction as the unit vector π’ hat towards the right of the screen. Therefore, π sub π₯ is equal to six.

Now we can do the same thing to find π sub π¦. This time we can start from the end of our horizontal component and then count grid squares vertically until we reach the tip of π. So thatβs one, two, three units. And note that this time we were going down, which is the opposite direction to the unit vector π£ hat, which is one unit upwards towards the top of the screen. Therefore, the vertical component π sub π¦ is equal to negative three. So we can now insert these numbers, and we have π is equal to six π’ hat minus three π£ hat. And now we have the vector π written in component form.