Vector 𝐚 equals negative three, two and vector 𝐛 equals negative two, five. Calculate vector 𝐚 minus three vector 𝐛, giving your answer as a column vector.
So in this question, what we’re actually asked to do is subtract three multiplied by vector 𝐛 from vector 𝐚. Okay, so let’s set this up. So first of all, we have the column vector negative three, two, because this represents our vector 𝐚, then minus three multiplied by our vector 𝐛, which is a column vector negative two, five. So the column vectors actually represent our vectors 𝐚 and 𝐛.
Okay, great! So what do we do at this stage? So first of all, we’re actually gonna look at three multiplied by the vector negative two, five. So this is actually a scalar multiplied by a vector. So what we do with this is we actually multiply each of the components of our column vector by three. So we have three multiplied by negative two and three multiplied by five. So therefore, what we’re gonna have is a column vector negative three, two minus a column vector negative six, 15. And that’s cause, as we said, three multiplied by negative two is negative six and three multiplied by five is 15.
Okay, great! So now what’s the next step? So then what we do is actually deal with the horizontal and the vertical components of our column vectors individually. So first of all, we have negative three minus negative six, and then we also have two minus 15. So this is gonna give us a final column vector of three, negative 13, and that’s actually because we had negative three minus negative six.
Well, minus a negative turns into a plus. So we have negative three plus six, which gives us three, and then two minus 15, which is actually negative 13. So therefore, we’ve solved the problem. We can say that vector 𝐚 minus three multiplied by vector 𝐛, if vector 𝐚 is negative three, two and vector 𝐛 is negative two, five, is equal to three, negative 13.