Video Transcript
Consider two vectors 𝐀 and 𝐁, where 𝐀 equals negative four 𝐢 hat minus two 𝐣 hat and 𝐁 equals negative eight 𝐢 hat minus nine 𝐣 hat. Calculate 𝐀 minus 𝐁.
This question gives us two vectors 𝐀 and 𝐁 in component form and asks us to find the result when we subtract the vector 𝐁 from the vector 𝐀. So, we have our two vectors 𝐀 and 𝐁. And if we recall that 𝐢 hat is the unit vector in the 𝑥-direction and 𝐣 hat is the unit vector in the 𝑦-direction, then we can see that each of our vectors 𝐀 and 𝐁 has an 𝑥-component and a 𝑦-component. Now, the question asks us to calculate 𝐀 minus 𝐁. So that’s the result we get when we subtract the vector 𝐁 from the vector 𝐀.
We should recall that if we want to subtract one vector from another, then we can do this by subtracting the 𝑥-components and the 𝑦-components of those vectors separately. So, with this in mind, let’s work out 𝐀 minus 𝐁. First, subtracting the 𝑥-components, we’re going to have the 𝑥-component of 𝐀, which is negative four, minus the 𝑥-component of 𝐁, which is negative eight. And since this is our 𝑥-component, we need to multiply this by our unit vector 𝐢 hat. Now subtracting the 𝑦-components, we have the 𝑦-component of 𝐀, which is negative two, and we need to subtract from this the 𝑦-component of 𝐁, which is negative nine. And then since this is the 𝑦-component. This gets multiplied by the unit vector 𝐣 hat.
If we now evaluate this 𝑥-component and this 𝑦-component, then taking care over the negative signs, we find that for the 𝑥-component negative four minus negative eight gives us positive four and for the 𝑦-component negative two minus negative nine gives us positive seven. So, our answer to the question is that the result when we calculate 𝐀 minus 𝐁 is four 𝐢 hat plus seven 𝐣 hat.
