Video Transcript
Consider the three vectors 𝐀, 𝐁, and 𝐂. 𝐀 is equal to two 𝐢 hat plus seven 𝐣 hat, 𝐁 is equal to negative four 𝐢 hat plus eight 𝐣 hat, and 𝐂 is equal to six 𝐢 hat minus nine 𝐣 hat. Which of the vectors shown in the diagram is equal to 𝐀 plus 𝐁 plus 𝐂? The grid squares in the diagram have a side length of one.
Let’s start by writing out the vectors 𝐀, 𝐁, and 𝐂 beneath each other like this. And we can then add them together by summing their components individually. For the horizontal component, we have two minus four plus six, which gives us four 𝐢 hat. And then for the vertical component, we have seven plus eight minus nine, which is equal to positive six 𝐣 hat.
We can then draw this resulting vector onto our diagram by counting one, two, three, four in the horizontal direction and one, two, three, four, five, six in the vertical direction. That makes this our resulting vector, which is equal to 𝐐 given in the diagram. So the vector shown in the diagram that’s equal to 𝐀 plus 𝐁 plus 𝐂 is vector 𝐐.
