# Question Video: Adding Two Vectors Given on a Grid Physics

The diagram shows two vectors, π and π. The grid squares in the diagram have a side length of 1. What is π + π in component form?

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### Video Transcript

The diagram shows two vectors π and π. The grid squares in the diagram have a side length of one. What is π plus π in component form?

Now, there are two methods we can use to approach this question. So letβs first do it the graphical way. Weβll do this using the tip-to-tail method, where we start from the tip of vector π and then weβre going to slide vector π over so that the tail of vector π touches the tip of vector π.

Now, when moving a vector, we have to be careful to ensure it stays the same size. So letβs first count the grid squares in vector π. Weβre going one, two, three vertically and then negative one, two, three horizontally. Now, if we redraw vector π starting from the tip of vector π, we end up with this new vector π. We can then draw in our resultant vector, which goes from the tail of vector π to the tip of the new vector π. And this is our resultant vector π plus π.

To write this resultant vector in component form, we then count grid squares of the resultant vector. We have negative one in the horizontal direction, so that gives us negative one π’ hat, and then negative one, two in the vertical direction, which gives us minus two π£ hat. And so π plus π in component form is negative one π’ hat minus two π£ hat.

Now, we could also have approached this question by summing components. Vector π in component form is one, two in the horizontal direction, which gives us two π’ hat, and negative one, two, three, four, five in the vertical direction, giving us minus five π£ hat. Vector π is negative one, two, three horizontally, so thatβs negative three π’ hat, and positive one, two, three vertically, so we have plus three π£ hat.

Now, we add these together by summing the components individually. So we have two plus negative three, which gives us negative one π’ hat, and then negative five plus three, which gives us negative two π£ hat.

So we can see that both methods give us the same answer that π plus π is equal to negative one π’ hat minus two π£ hat.