Video: Subtracting Vectors Using a Grid

The diagram shows seven vectors 𝐀, 𝐁, 𝐏, 𝐐, 𝐑, 𝐒, and 𝐓. Which of the vectors is equal to 𝐀 βˆ’ 𝐁?

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Video Transcript

The diagram shows seven vectors 𝐀, 𝐁, 𝐏, 𝐐, 𝐑, 𝐒, and 𝐓. Which of the vectors is equal to 𝐀 minus 𝐁?

We are being asked to find the vector resultant of vector 𝐀 minus vector 𝐁. Since our vectors have been given to us graphically, we can solve for the vector subtraction using a graphical method. We need to remember that when we’re subtracting vector 𝐁 from vector 𝐀, it’s the same thing as adding the negative of vector 𝐁 to vector 𝐀. To solve our problem, we are going to need to draw in a vector that’s the negative of vector 𝐁. A negative vector is a vector that is rotated 180 degrees from the original vector. Vector 𝐁 had a magnitude of three units to the right of the screen. Therefore, vector negative 𝐁 will have a value of three units to the left of the screen. Vector 𝐁 also had a length of five units to the top of our screen and therefore vector negative 𝐁 will have a value of five units to the bottom of the screen.

Now that we have drawn in vector negative 𝐁, we can add vector 𝐀 and vector negative 𝐁 together using the tip-to-tail method. In the tip-to-tail method, one vector slides over until its tail is on the tip of the other vector. The resultant is drawn from the tail of the unmoved vector to the tip of the moved vector. For our problem, we’re gonna slide vector negative 𝐁 over until it’s on the tip of vector 𝐀. Then, we draw in a resultant vector from the tail of vector 𝐀 to the tip of vector negative 𝐁. The resultant points away from the origin towards the tip of vector negative 𝐁. We can see that vector 𝐐 overlaps our resultant for vector 𝐀 minus vector 𝐁. Therefore, we can say that of the seven vectors shown vector 𝐐 is equal to vector 𝐀 minus vector 𝐁.

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