Video Transcript
Some vectors are drawn to scale on a square grid. Which color vector shows the resultant of the black vectors 𝐀 and 𝐁? Is it (a) blue, (b) green, (c) red, or (d) orange?
When we combine two vectors, we use the tip-to-tail method. So we start from the tip of vector 𝐀, and then we’re going to slide vector 𝐁 over so that its tail joins to the tip of 𝐀. So let’s first count out the components of 𝐁 to make sure that we’re keeping it the same size. If each grid square is one unit, then vector 𝐁 has a horizontal component of one, two, three, four, five units and a vertical component of one, two, three. If we count out those same components starting from the tip of vector 𝐀, then we have one, two, three, four, five in the horizontal direction and one, two, three vertically. And so we would draw in our new vector 𝐁 here.
The resultant of the two vectors 𝐀 and 𝐁 then goes from the tail of vector 𝐀, which is at the origin, up to the tip of the new vector 𝐁. And that resultant vector is shown by (c), the red vector.
