### Video Transcript

Given that vector 𝐴 equals
negative two, two; vector 𝐵 equals five, two; and vector 𝐶 equals negative three,
negative two, find negative vector 𝐴 plus vector 𝐵 minus vector 𝐶.

Whenever we’re looking to solve a
problem that’s adding and subtracting vectors, what we want to do is actually split
it into its component parts. So we’re gonna begin by looking at
the 𝑥 components. So our first term is negative
negative two — and this is because it’s negative vector 𝐴 — plus five, because
that’s the 𝑥-component of vector 𝐵, and then minus negative three. And that’s because this is the
𝑥-component of vector 𝐶. And again, we’ve got minus and
negative.

Okay, now we can move on to the
𝑦-components of our vectors. So we’re gonna start with negative
two — and that’s because it’s minus vector 𝐴 — then plus two — because this is the
𝑦-component of vector 𝐵. And then, finally, we have the
𝑦-component of vector 𝐶. So we’ve got minus negative
two. And again, it’s negative negative
because we’re subtracting the final vector.

Okay, great! So now what we want to do is
actually calculate each of our components. So for our 𝑥-component, we have
two plus five plus three. And that’s because I’ve just tidied
it up because we had minus and negative, which makes a positive, four minus negative
two and minus negative three. And then for our 𝑦-component, we
have negative two plus two plus two. And again, we got this because
you’re subtracting a negative. So therefore, it turns
positive.

So therefore, we can say that,
given that vector 𝐴 equals negative two, two; vector 𝐵 equals five, two; and
vector 𝐶 equals negative three, negative two, then minus vector 𝐴 plus vector 𝐵
minus vector 𝐶 is equal to 10, two, where our 𝑥-component is 10 and our
𝑦-component is two.